6(x^2-3x-4)=0

Solution for 6(x^2-3x-4)=0 equation:

6(x^2-3x-4)=0

We multiply parentheses

6x^2-18x-24=0

a = 6; b = -18; c = -24;
Δ = b2-4ac
Δ = -182-4·6·(-24)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*6}=\frac{48}{12}
=4
$