6x+6=4x2

Solution for 6x+6=4x2 equation:

6x+6=4x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-4x^2+6x+6=0

a = -4; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-4)·6
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*-4}=\frac{-6-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-4}=\frac{-6+2\sqrt{33}}{-8}
$