3x^2-6x+4=31

Solution for 3x^2-6x+4=31 equation:

3x^2-6x+4=31

We move all terms to the left:

3x^2-6x+4-(31)=0

We add all the numbers together, and all the variables

3x^2-6x-27=0

a = 3; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·3·(-27)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{10}}{2*3}=\frac{6-6\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{10}}{2*3}=\frac{6+6\sqrt{10}}{6}
$