a(a+64)=180

Solution for a(a+64)=180 equation:

a(a+64)=180

We move all terms to the left:

a(a+64)-(180)=0

We multiply parentheses

a^2+64a-180=0

a = 1; b = 64; c = -180;
Δ = b2-4ac
Δ = 642-4·1·(-180)
Δ = 4816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4816}=\sqrt{16*301}=\sqrt{16}*\sqrt{301}=4\sqrt{301}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{301}}{2*1}=\frac{-64-4\sqrt{301}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{301}}{2*1}=\frac{-64+4\sqrt{301}}{2}
$