x*x-8*x=90

Solution for x*x-8*x=90 equation:

x*x-8x=90

We move all terms to the left:

x*x-8x-(90)=0

We add all the numbers together, and all the variables

-8x+x*x-90=0

Wy multiply elements

x^2-8x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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