5q+q^2=5+q

Solution for 5q+q^2=5+q equation:

5q+q^2=5+q

We move all terms to the left:

5q+q^2-(5+q)=0

We add all the numbers together, and all the variables

q^2+5q-(q+5)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

q^2+4q-5=0

a = 1; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*1}=\frac{-10}{2}
=-5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*1}=\frac{2}{2}
=1
$