45=3x^2+2x

Solution for 45=3x^2+2x equation:

45=3x^2+2x

We move all terms to the left:

45-(3x^2+2x)=0

We get rid of parentheses

-3x^2-2x+45=0

a = -3; b = -2; c = +45;
Δ = b2-4ac
Δ = -22-4·(-3)·45
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{34}}{2*-3}=\frac{2-4\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{34}}{2*-3}=\frac{2+4\sqrt{34}}{-6}
$