(x+13)(4x-7)=0

Solution for (x+13)(4x-7)=0 equation:

(x+13)(4x-7)=0

We multiply parentheses ..

(+4x^2-7x+52x-91)=0

We get rid of parentheses

4x^2-7x+52x-91=0

We add all the numbers together, and all the variables

4x^2+45x-91=0

a = 4; b = 45; c = -91;
Δ = b2-4ac
Δ = 452-4·4·(-91)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-59}{2*4}=\frac{-104}{8}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+59}{2*4}=\frac{14}{8}
=1+3/4
$