3x^2-4x+6=36

Solution for 3x^2-4x+6=36 equation:

3x^2-4x+6=36

We move all terms to the left:

3x^2-4x+6-(36)=0

We add all the numbers together, and all the variables

3x^2-4x-30=0

a = 3; b = -4; c = -30;
Δ = b2-4ac
Δ = -42-4·3·(-30)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*3}=\frac{4-2\sqrt{94}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*3}=\frac{4+2\sqrt{94}}{6}
$