6x(x-4)=30

Solution for 6x(x-4)=30 equation:

6x(x-4)=30

We move all terms to the left:

6x(x-4)-(30)=0

We multiply parentheses

6x^2-24x-30=0

a = 6; b = -24; c = -30;
Δ = b2-4ac
Δ = -242-4·6·(-30)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*6}=\frac{60}{12}
=5
$