2x(x-50)=2500

Solution for 2x(x-50)=2500 equation:

2x(x-50)=2500

We move all terms to the left:

2x(x-50)-(2500)=0

We multiply parentheses

2x^2-100x-2500=0

a = 2; b = -100; c = -2500;
Δ = b2-4ac
Δ = -1002-4·2·(-2500)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100\sqrt{3}}{2*2}=\frac{100-100\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100\sqrt{3}}{2*2}=\frac{100+100\sqrt{3}}{4}
$