5-3q+2q^2=3q^2-q+3

Solution for 5-3q+2q^2=3q^2-q+3 equation:

5-3q+2q^2=3q^2-q+3

We move all terms to the left:

5-3q+2q^2-(3q^2-q+3)=0

We get rid of parentheses

2q^2-3q^2-3q+q-3+5=0

We add all the numbers together, and all the variables

-1q^2-2q+2=0

a = -1; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-1)·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-1}=\frac{2-2\sqrt{3}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-1}=\frac{2+2\sqrt{3}}{-2}
$