6x^2-30x+42=6

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

6x^2-30x+42=6

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x^2-30x+36=0

a = 6; b = -30; c = +36;
Δ = b2-4ac
Δ = -302-4·6·36
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6}{2*6}=\frac{24}{12}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6}{2*6}=\frac{36}{12}
=3
$