(3x-1)(x+8)=0

Solution for (3x-1)(x+8)=0 equation:

(3x-1)(x+8)=0

We multiply parentheses ..

(+3x^2+24x-1x-8)=0

We get rid of parentheses

3x^2+24x-1x-8=0

We add all the numbers together, and all the variables

3x^2+23x-8=0

a = 3; b = 23; c = -8;
Δ = b2-4ac
Δ = 232-4·3·(-8)
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{-(23)-25}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+25}{2*3}=\frac{2}{6}
=1/3
$