q2+30q=-4q2+10q+13500

Solution for q2+30q=-4q2+10q+13500 equation:

q2+30q=-4q^2+10q+13500

We move all terms to the left:

q2+30q-(-4q^2+10q+13500)=0

We add all the numbers together, and all the variables

q^2-(-4q^2+10q+13500)+30q=0

We get rid of parentheses

q^2+4q^2-10q+30q-13500=0

We add all the numbers together, and all the variables

5q^2+20q-13500=0

a = 5; b = 20; c = -13500;
Δ = b2-4ac
Δ = 202-4·5·(-13500)
Δ = 270400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{270400}=520$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-520}{2*5}=\frac{-540}{10}
=-54
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+520}{2*5}=\frac{500}{10}
=50
$