6=12x^2-36x+10

Solution for 6=12x^2-36x+10 equation:

6=12x^2-36x+10

We move all terms to the left:

6-(12x^2-36x+10)=0

We get rid of parentheses

-12x^2+36x-10+6=0

We add all the numbers together, and all the variables

-12x^2+36x-4=0

a = -12; b = 36; c = -4;
Δ = b2-4ac
Δ = 362-4·(-12)·(-4)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{69}}{2*-12}=\frac{-36-4\sqrt{69}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{69}}{2*-12}=\frac{-36+4\sqrt{69}}{-24}
$