6-4x=3x^2

Solution for 6-4x=3x^2 equation:

6-4x=3x^2

We move all terms to the left:

6-4x-(3x^2)=0

determiningTheFunctionDomain
-3x^2-4x+6=0

a = -3; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-3)·6
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*-3}=\frac{4-2\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*-3}=\frac{4+2\sqrt{22}}{-6}
$