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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+19x-40=0

a = 3; b = 19; c = -40;
Δ = b2-4ac
Δ = 192-4·3·(-40)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*3}=\frac{10}{6}
=1+2/3
$