3x=2x^2-6

Solution for 3x=2x^2-6 equation:

3x=2x^2-6

We move all terms to the left:

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

We get rid of parentheses

-2x^2+3x+6=0

a = -2; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-2)·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{57}}{2*-2}=\frac{-3-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-2}=\frac{-3+\sqrt{57}}{-4}
$