(20x)(x+50)=5000

Solution for (20x)(x+50)=5000 equation:

(20x)(x+50)=5000

We move all terms to the left:

(20x)(x+50)-(5000)=0

We multiply parentheses

20x^2+1000x-5000=0

a = 20; b = 1000; c = -5000;
Δ = b2-4ac
Δ = 10002-4·20·(-5000)
Δ = 1400000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1400000}=\sqrt{40000*35}=\sqrt{40000}*\sqrt{35}=200\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-200\sqrt{35}}{2*20}=\frac{-1000-200\sqrt{35}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+200\sqrt{35}}{2*20}=\frac{-1000+200\sqrt{35}}{40}
$