7q^2-6q=6q^2-8q+35

Solution for 7q^2-6q=6q^2-8q+35 equation:

7q^2-6q=6q^2-8q+35

We move all terms to the left:

7q^2-6q-(6q^2-8q+35)=0

We get rid of parentheses

7q^2-6q^2-6q+8q-35=0

We add all the numbers together, and all the variables

q^2+2q-35=0

a = 1; b = 2; c = -35;
Δ = b2-4ac
Δ = 22-4·1·(-35)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*1}=\frac{-14}{2}
=-7
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*1}=\frac{10}{2}
=5
$