q^2-8q-4=5

Solution for q^2-8q-4=5 equation:

q^2-8q-4=5

We move all terms to the left:

q^2-8q-4-(5)=0

We add all the numbers together, and all the variables

q^2-8q-9=0

a = 1; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·1·(-9)
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{-(-8)-10}{2*1}=\frac{-2}{2}
=-1
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*1}=\frac{18}{2}
=9
$