20c(c-50)=19000

Solution for 20c(c-50)=19000 equation:

20c(c-50)=19000

We move all terms to the left:

20c(c-50)-(19000)=0

We multiply parentheses

20c^2-1000c-19000=0

a = 20; b = -1000; c = -19000;
Δ = b2-4ac
Δ = -10002-4·20·(-19000)
Δ = 2520000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2520000}=\sqrt{360000*7}=\sqrt{360000}*\sqrt{7}=600\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-600\sqrt{7}}{2*20}=\frac{1000-600\sqrt{7}}{40}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+600\sqrt{7}}{2*20}=\frac{1000+600\sqrt{7}}{40}
$