6x+6x^2=84

Solution for 6x+6x^2=84 equation:

6x+6x^2=84

We move all terms to the left:

6x+6x^2-(84)=0

a = 6; b = 6; c = -84;
Δ = b2-4ac
Δ = 62-4·6·(-84)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{57}}{2*6}=\frac{-6-6\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{57}}{2*6}=\frac{-6+6\sqrt{57}}{12}
$