9q2-11q+2=-3q2

Solution for 9q2-11q+2=-3q2 equation:

9q^2-11q+2=-3q^2

We move all terms to the left:

9q^2-11q+2-(-3q^2)=0

We get rid of parentheses

9q^2+3q^2-11q+2=0

We add all the numbers together, and all the variables

12q^2-11q+2=0

a = 12; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·12·2
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{-(-11)-5}{2*12}=\frac{6}{24}
=1/4
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*12}=\frac{16}{24}
=2/3
$