6x^2=66x-42

Solution for 6x^2=66x-42 equation:

6x^2=66x-42

We move all terms to the left:

6x^2-(66x-42)=0

We get rid of parentheses

6x^2-66x+42=0

a = 6; b = -66; c = +42;
Δ = b2-4ac
Δ = -662-4·6·42
Δ = 3348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3348}=\sqrt{36*93}=\sqrt{36}*\sqrt{93}=6\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{93}}{2*6}=\frac{66-6\sqrt{93}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{93}}{2*6}=\frac{66+6\sqrt{93}}{12}
$