6X^2+4x-4=31

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

6X^2+4X-4=31

We move all terms to the left:

6X^2+4X-4-(31)=0

We add all the numbers together, and all the variables

6X^2+4X-35=0

a = 6; b = 4; c = -35;
Δ = b2-4ac
Δ = 42-4·6·(-35)
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{214}}{2*6}=\frac{-4-2\sqrt{214}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{214}}{2*6}=\frac{-4+2\sqrt{214}}{12}
$