6x^2-48x+42=-30

Solution for 6x^2-48x+42=-30 equation:

6x^2-48x+42=-30

We move all terms to the left:

6x^2-48x+42-(-30)=0

We add all the numbers together, and all the variables

6x^2-48x+72=0

a = 6; b = -48; c = +72;
Δ = b2-4ac
Δ = -482-4·6·72
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24}{2*6}=\frac{24}{12}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24}{2*6}=\frac{72}{12}
=6
$