q^2-9q-23=-5-2q

Solution for q^2-9q-23=-5-2q equation:

q^2-9q-23=-5-2q

We move all terms to the left:

q^2-9q-23-(-5-2q)=0

We add all the numbers together, and all the variables

q^2-9q-(-2q-5)-23=0

We get rid of parentheses

q^2-9q+2q+5-23=0

We add all the numbers together, and all the variables

q^2-7q-18=0

a = 1; b = -7; c = -18;
Δ = b2-4ac
Δ = -72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*1}=\frac{-4}{2}
=-2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*1}=\frac{18}{2}
=9
$