(7x+15)(x+13)=180

Solution for (7x+15)(x+13)=180 equation:

(7x+15)(x+13)=180

We move all terms to the left:

(7x+15)(x+13)-(180)=0

We multiply parentheses ..

(+7x^2+91x+15x+195)-180=0

We get rid of parentheses

7x^2+91x+15x+195-180=0

We add all the numbers together, and all the variables

7x^2+106x+15=0

a = 7; b = 106; c = +15;
Δ = b2-4ac
Δ = 1062-4·7·15
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-104}{2*7}=\frac{-210}{14}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+104}{2*7}=\frac{-2}{14}
=-1/7
$