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

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

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

We multiply parentheses ..

(+24x^2+9x-24x-9)=0

We get rid of parentheses

24x^2+9x-24x-9=0

We add all the numbers together, and all the variables

24x^2-15x-9=0

a = 24; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·24·(-9)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-33}{2*24}=\frac{-18}{48}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+33}{2*24}=\frac{48}{48}
=1
$