3x^2+6x=81

Solution for 3x^2+6x=81 equation:

3x^2+6x=81

We move all terms to the left:

3x^2+6x-(81)=0

a = 3; b = 6; c = -81;
Δ = b2-4ac
Δ = 62-4·3·(-81)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{7}}{2*3}=\frac{-6-12\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{7}}{2*3}=\frac{-6+12\sqrt{7}}{6}
$