50=30q+q^2

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

50=30q+q^2

We move all terms to the left:

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

We get rid of parentheses

-q^2-30q+50=0

We add all the numbers together, and all the variables

-1q^2-30q+50=0

a = -1; b = -30; c = +50;
Δ = b2-4ac
Δ = -302-4·(-1)·50
Δ = 1100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{11}}{2*-1}=\frac{30-10\sqrt{11}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{11}}{2*-1}=\frac{30+10\sqrt{11}}{-2}
$