(x+13)(x+23)=90

Solution for (x+13)(x+23)=90 equation:

(x+13)(x+23)=90

We move all terms to the left:

(x+13)(x+23)-(90)=0

We multiply parentheses ..

(+x^2+23x+13x+299)-90=0

We get rid of parentheses

x^2+23x+13x+299-90=0

We add all the numbers together, and all the variables

x^2+36x+209=0

a = 1; b = 36; c = +209;
Δ = b2-4ac
Δ = 362-4·1·209
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{-(36)-2\sqrt{115}}{2*1}=\frac{-36-2\sqrt{115}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{115}}{2*1}=\frac{-36+2\sqrt{115}}{2}
$