6q^2-13q+6=2q^2

Solution for 6q^2-13q+6=2q^2 equation:

6q^2-13q+6=2q^2

We move all terms to the left:

6q^2-13q+6-(2q^2)=0

determiningTheFunctionDomain
6q^2-2q^2-13q+6=0

We add all the numbers together, and all the variables

4q^2-13q+6=0

a = 4; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·4·6
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{73}}{2*4}=\frac{13-\sqrt{73}}{8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{73}}{2*4}=\frac{13+\sqrt{73}}{8}
$