2(27x-42)=6x^2

Solution for 2(27x-42)=6x^2 equation:

2(27x-42)=6x^2

We move all terms to the left:

2(27x-42)-(6x^2)=0

determiningTheFunctionDomain
-6x^2+2(27x-42)=0

We multiply parentheses

-6x^2+54x-84=0

a = -6; b = 54; c = -84;
Δ = b2-4ac
Δ = 542-4·(-6)·(-84)
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{-(54)-30}{2*-6}=\frac{-84}{-12}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30}{2*-6}=\frac{-24}{-12}
=+2
$