(x+10)(x+8)=90

Solution for (x+10)(x+8)=90 equation:

(x+10)(x+8)=90

We move all terms to the left:

(x+10)(x+8)-(90)=0

We multiply parentheses ..

(+x^2+8x+10x+80)-90=0

We get rid of parentheses

x^2+8x+10x+80-90=0

We add all the numbers together, and all the variables

x^2+18x-10=0

a = 1; b = 18; c = -10;
Δ = b2-4ac
Δ = 182-4·1·(-10)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{91}}{2*1}=\frac{-18-2\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{91}}{2*1}=\frac{-18+2\sqrt{91}}{2}
$