Solve 45-a=5sqrt{225+(d+15)^2}

$$45 - a = 5 \sqrt { 225 + ( d + 15 ) ^ { 2 } }$$

Solve for a

$$a=-5\sqrt{d^{2}+30d+450}+45$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(d+15\right)^{2}.

$$45-a=5\sqrt{225+d^{2}+30d+225}$$

Add 225 and 225 to get 450.

$$45-a=5\sqrt{450+d^{2}+30d}$$

Subtract 45 from both sides.

$$-a=5\sqrt{450+d^{2}+30d}-45$$

The equation is in standard form.

$$-a=5\sqrt{d^{2}+30d+450}-45$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{5\sqrt{d^{2}+30d+450}-45}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{5\sqrt{d^{2}+30d+450}-45}{-1}$$

Divide 5\sqrt{450+d^{2}+30d}-45 by -1.

$$a=-5\sqrt{d^{2}+30d+450}+45$$

Solve for d

$$d=\frac{\sqrt{\left(a-120\right)\left(a+30\right)}-75}{5}$$

$$d=\frac{-\sqrt{\left(a-120\right)\left(a+30\right)}-75}{5}\text{, }a\leq -30$$