5(x+8)(x+13)=0

Solution for 5(x+8)(x+13)=0 equation:

5(x+8)(x+13)=0

We multiply parentheses ..

5(+x^2+13x+8x+104)=0

We multiply parentheses

5x^2+65x+40x+520=0

We add all the numbers together, and all the variables

5x^2+105x+520=0

a = 5; b = 105; c = +520;
Δ = b2-4ac
Δ = 1052-4·5·520
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-25}{2*5}=\frac{-130}{10}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+25}{2*5}=\frac{-80}{10}
=-8
$