2/3 √9x+45 - 5√2x+10 /8  = -3/3

To assist with the equations you've provided, let's solve each one step by step.

### a.
\[
\frac{2}{3} \sqrt{9x + 45} - \frac{5 \sqrt{2x + 10}}{8} = -\frac{3}{3}
\]

This simplifies to:
\[
\frac{2}{3} \sqrt{9x + 45} - \frac{5 \sqrt{2x + 10}}{8} = -1
\]

Now, let's isolate one of the terms:
\[
\frac{2}{3} \sqrt{9x + 45} = -1 + \frac{5 \sqrt{2x + 10}}{8}
\]

Multiply everything by the common denominator (24) to eliminate the fractions:
\[
24 \cdot \frac{2}{3} \sqrt{9x + 45} = 24 \cdot (-1) + 24 \cdot \frac{5 \sqrt{2x + 10}}{8}
\]
\[
16 \sqrt{9x + 45} = -24 + 15 \sqrt{2x + 10}
\]

Isolate \(\sqrt{9x + 45}\):
\[
16 \sqrt{9x + 45} + 24 = 15 \sqrt{2x + 10}
\]

Square both sides and solve for \(x\):
\[
(16 \sqrt{9x + 45} + 24)^2 = (15 \sqrt{2x + 10})^2
\]

Continue solving to find \(x\).

---

### b.
\[
\sqrt{x - 4} - 2\sqrt{4x - 16} + 3\sqrt{9x - 36} = 10
\]

First, notice that:
\[
4x - 16 = 4(x - 4), \quad \text{and} \quad 9x - 36 = 9(x - 4)
\]
So we can substitute to solve. Let \(y = \sqrt{x - 4}\), then:
\[
y - 2(2y) + 3(3y) = 10
\]
\[
y - 4y + 9y = 10
\]
\[
6y = 10 \implies y = \frac{10}{6} = \frac{5}{3}
\]

Now revert back to find \(x\):
\[
\sqrt{x - 4} = \frac{5}{3} \implies x - 4 = \left(\frac{5}{3}\right)^2 = \frac{25}{9} \implies x = 4 + \frac{25}{9} = \frac{36}{9} + \frac{25}{9} = \frac{61}{9}
\]

---

### c.
\[
\sqrt{2x + 1} + \sqrt{8x + 4} = 6
\]

Notice that:
\[
\sqrt{8x + 4} = 2\sqrt{2x + 1} \implies \sqrt{2x + 1} + 2\sqrt{2x + 1} = 6
\]
\[
3\sqrt{2x + 1} = 6 \implies \sqrt{2x + 1} = 2 \implies 2x + 1 = 4 \implies 2x = 3 \implies x = \frac{3}{2}
\]

---

### d.
\[
\frac{3}{4} \sqrt{4x + 12} - \frac{3 \sqrt{25x + 75}}{9} = -\frac{5}{2}
\]

Multiply through by the common denominator (36):
\[
27 \sqrt{4x + 12} - 12 \sqrt{25x + 75} = -90
\]

Isolate one of the square root terms and then square both sides to solve for \(x\).

---

### e.
\[
4\sqrt{6 - x} - \sqrt{24 - 4x} + 3\sqrt{54 - 9x} = 11
\]

You can simplify the square roots before isolating and squaring them as well.

For each equation, follow the appropriate steps to isolate the variables, simplify, then solve the resulting algebraic expressions. Please let me know if you'd like to see any specific equation worked through in detail!