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

Solution for 3(2x+1)(x-8)=0 equation:

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

We multiply parentheses ..

3(+2x^2-16x+x-8)=0

We multiply parentheses

6x^2-48x+3x-24=0

We add all the numbers together, and all the variables

6x^2-45x-24=0

a = 6; b = -45; c = -24;
Δ = b2-4ac
Δ = -452-4·6·(-24)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*6}=\frac{96}{12}
=8
$