8q^2-5=7q^2-9q+12

Solution for 8q^2-5=7q^2-9q+12 equation:

8q^2-5=7q^2-9q+12

We move all terms to the left:

8q^2-5-(7q^2-9q+12)=0

We get rid of parentheses

8q^2-7q^2+9q-12-5=0

We add all the numbers together, and all the variables

q^2+9q-17=0

a = 1; b = 9; c = -17;
Δ = b2-4ac
Δ = 92-4·1·(-17)
Δ = 149
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{-(9)-\sqrt{149}}{2*1}=\frac{-9-\sqrt{149}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{149}}{2*1}=\frac{-9+\sqrt{149}}{2}
$