8q=q^2-7

Solution for 8q=q^2-7 equation:

8q=q^2-7

We move all terms to the left:

8q-(q^2-7)=0

We get rid of parentheses

-q^2+8q+7=0

We add all the numbers together, and all the variables

-1q^2+8q+7=0

a = -1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·(-1)·7
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{23}}{2*-1}=\frac{-8-2\sqrt{23}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{23}}{2*-1}=\frac{-8+2\sqrt{23}}{-2}
$