50q=30q+q^2

Solution for 50q=30q+q^2 equation:

50q=30q+q^2

We move all terms to the left:

50q-(30q+q^2)=0

We get rid of parentheses

-q^2-30q+50q=0

We add all the numbers together, and all the variables

-1q^2+20q=0

a = -1; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-1)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-1}=\frac{-40}{-2}
=+20
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-1}=\frac{0}{-2}
=0
$