(x-13)(x+23)=0

Solution for (x-13)(x+23)=0 equation:

(x-13)(x+23)=0

We multiply parentheses ..

(+x^2+23x-13x-299)=0

We get rid of parentheses

x^2+23x-13x-299=0

We add all the numbers together, and all the variables

x^2+10x-299=0

a = 1; b = 10; c = -299;
Δ = b2-4ac
Δ = 102-4·1·(-299)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-36}{2*1}=\frac{-46}{2}
=-23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+36}{2*1}=\frac{26}{2}
=13
$