8x+(x^2-9)=90

Solution for 8x+(x^2-9)=90 equation:

8x+(x^2-9)=90

We move all terms to the left:

8x+(x^2-9)-(90)=0

We get rid of parentheses

x^2+8x-9-90=0

We add all the numbers together, and all the variables

x^2+8x-99=0

a = 1; b = 8; c = -99;
Δ = b2-4ac
Δ = 82-4·1·(-99)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{115}}{2*1}=\frac{-8-2\sqrt{115}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{115}}{2*1}=\frac{-8+2\sqrt{115}}{2}
$