2x^2-500x=-300

Solution for 2x^2-500x=-300 equation:

2x^2-500x=-300

We move all terms to the left:

2x^2-500x-(-300)=0

We add all the numbers together, and all the variables

2x^2-500x+300=0

a = 2; b = -500; c = +300;
Δ = b2-4ac
Δ = -5002-4·2·300
Δ = 247600
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:

$\sqrt{\Delta}=\sqrt{247600}=\sqrt{400*619}=\sqrt{400}*\sqrt{619}=20\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-20\sqrt{619}}{2*2}=\frac{500-20\sqrt{619}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+20\sqrt{619}}{2*2}=\frac{500+20\sqrt{619}}{4}
$