3q2=7q-2

Solution for 3q2=7q-2 equation:

3q^2=7q-2

We move all terms to the left:

3q^2-(7q-2)=0

We get rid of parentheses

3q^2-7q+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$