8q+6=6q+4q^2

Solution for 8q+6=6q+4q^2 equation:

8q+6=6q+4q^2

We move all terms to the left:

8q+6-(6q+4q^2)=0

We get rid of parentheses

-4q^2-6q+8q+6=0

We add all the numbers together, and all the variables

-4q^2+2q+6=0

a = -4; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-4)·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-4}=\frac{8}{-8}
=-1
$