-a^2-8a+90=0

Solution for -a^2-8a+90=0 equation:

-a^2-8a+90=0

We add all the numbers together, and all the variables

-1a^2-8a+90=0

a = -1; b = -8; c = +90;
Δ = b2-4ac
Δ = -82-4·(-1)·90
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{106}}{2*-1}=\frac{8-2\sqrt{106}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{106}}{2*-1}=\frac{8+2\sqrt{106}}{-2}
$