3q^2+2q=5

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

3q^2+2q=5

We move all terms to the left:

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

a = 3; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·3·(-5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*3}=\frac{-10}{6}
=-1+2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*3}=\frac{6}{6}
=1
$