-2a(6a+5)+16=-90

Solution for -2a(6a+5)+16=-90 equation:

-2a(6a+5)+16=-90

We move all terms to the left:

-2a(6a+5)+16-(-90)=0

We add all the numbers together, and all the variables

-2a(6a+5)+106=0

We multiply parentheses

-12a^2-10a+106=0

a = -12; b = -10; c = +106;
Δ = b2-4ac
Δ = -102-4·(-12)·106
Δ = 5188
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:

$\sqrt{\Delta}=\sqrt{5188}=\sqrt{4*1297}=\sqrt{4}*\sqrt{1297}=2\sqrt{1297}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1297}}{2*-12}=\frac{10-2\sqrt{1297}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1297}}{2*-12}=\frac{10+2\sqrt{1297}}{-24}
$