q^2-8q=3

Solution for q^2-8q=3 equation:

q^2-8q=3

We move all terms to the left:

q^2-8q-(3)=0

a = 1; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·1·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{19}}{2*1}=\frac{8-2\sqrt{19}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{19}}{2*1}=\frac{8+2\sqrt{19}}{2}
$