2x+2=3x2

Solution for 2x+2=3x2 equation:

2x+2=3x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-3x^2+2x+2=0

a = -3; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-3)·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-3}=\frac{-2-2\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-3}=\frac{-2+2\sqrt{7}}{-6}
$