(X+3)(x+13)=90

Solution for (X+3)(x+13)=90 equation:

(X+3)(X+13)=90

We move all terms to the left:

(X+3)(X+13)-(90)=0

We multiply parentheses ..

(+X^2+13X+3X+39)-90=0

We get rid of parentheses

X^2+13X+3X+39-90=0

We add all the numbers together, and all the variables

X^2+16X-51=0

a = 1; b = 16; c = -51;
Δ = b2-4ac
Δ = 162-4·1·(-51)
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{-(16)-2\sqrt{115}}{2*1}=\frac{-16-2\sqrt{115}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{115}}{2*1}=\frac{-16+2\sqrt{115}}{2}
$