(x-13)*(x+8)=196

Solution for (x-13)*(x+8)=196 equation:

(x-13)(x+8)=196

We move all terms to the left:

(x-13)(x+8)-(196)=0

We multiply parentheses ..

(+x^2+8x-13x-104)-196=0

We get rid of parentheses

x^2+8x-13x-104-196=0

We add all the numbers together, and all the variables

x^2-5x-300=0

a = 1; b = -5; c = -300;
Δ = b2-4ac
Δ = -52-4·1·(-300)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*1}=\frac{40}{2}
=20
$