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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+5x^2+40x-3x-24)), so:

(+5x^2+40x-3x-24)

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+37x-24

Back to the equation:

-(5x^2+37x-24)


We get rid of parentheses

-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
$