8q^2-2q=7q^2+5q+18

Solution for 8q^2-2q=7q^2+5q+18 equation:

8q^2-2q=7q^2+5q+18

We move all terms to the left:

8q^2-2q-(7q^2+5q+18)=0

We get rid of parentheses

8q^2-7q^2-2q-5q-18=0

We add all the numbers together, and all the variables

q^2-7q-18=0

a = 1; b = -7; c = -18;
Δ = b2-4ac
Δ = -72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*1}=\frac{-4}{2}
=-2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*1}=\frac{18}{2}
=9
$