20+2q^2=5-11q

Solution for 20+2q^2=5-11q equation:

20+2q^2=5-11q

We move all terms to the left:

20+2q^2-(5-11q)=0

We add all the numbers together, and all the variables

2q^2-(-11q+5)+20=0

We get rid of parentheses

2q^2+11q-5+20=0

We add all the numbers together, and all the variables

2q^2+11q+15=0

a = 2; b = 11; c = +15;
Δ = b2-4ac
Δ = 112-4·2·15
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*2}=\frac{-12}{4}
=-3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*2}=\frac{-10}{4}
=-2+1/2
$