(2x+6)(x-13)=0

Solution for (2x+6)(x-13)=0 equation:

(2x+6)(x-13)=0

We multiply parentheses ..

(+2x^2-26x+6x-78)=0

We get rid of parentheses

2x^2-26x+6x-78=0

We add all the numbers together, and all the variables

2x^2-20x-78=0

a = 2; b = -20; c = -78;
Δ = b2-4ac
Δ = -202-4·2·(-78)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-32}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+32}{2*2}=\frac{52}{4}
=13
$