8q^2-3q=7q^2-5q+48

Solution for 8q^2-3q=7q^2-5q+48 equation:

8q^2-3q=7q^2-5q+48

We move all terms to the left:

8q^2-3q-(7q^2-5q+48)=0

We get rid of parentheses

8q^2-7q^2-3q+5q-48=0

We add all the numbers together, and all the variables

q^2+2q-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$