3x^2=2x+33

Solution for 3x^2=2x+33 equation:

3x^2=2x+33

We move all terms to the left:

3x^2-(2x+33)=0

We get rid of parentheses

3x^2-2x-33=0

a = 3; b = -2; c = -33;
Δ = b2-4ac
Δ = -22-4·3·(-33)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-20}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+20}{2*3}=\frac{22}{6}
=3+2/3
$