5x(x-8)+3(x-8)=0

Solution for 5x(x-8)+3(x-8)=0 equation:

5x(x-8)+3(x-8)=0

We multiply parentheses

5x^2-40x+3x-24=0

We add all the numbers together, and all the variables

5x^2-37x-24=0

a = 5; b = -37; c = -24;
Δ = b2-4ac
Δ = -372-4·5·(-24)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-43}{2*5}=\frac{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+43}{2*5}=\frac{80}{10}
=8
$