(x+13)(2x-7)=0

Solution for (x+13)(2x-7)=0 equation:

(x+13)(2x-7)=0

We multiply parentheses ..

(+2x^2-7x+26x-91)=0

We get rid of parentheses

2x^2-7x+26x-91=0

We add all the numbers together, and all the variables

2x^2+19x-91=0

a = 2; b = 19; c = -91;
Δ = b2-4ac
Δ = 192-4·2·(-91)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-33}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+33}{2*2}=\frac{14}{4}
=3+1/2
$