300x=x^2-40x+610

Solution for 300x=x^2-40x+610 equation:

300x=x^2-40x+610

We move all terms to the left:

300x-(x^2-40x+610)=0

We get rid of parentheses

-x^2+300x+40x-610=0

We add all the numbers together, and all the variables

-1x^2+340x-610=0

a = -1; b = 340; c = -610;
Δ = b2-4ac
Δ = 3402-4·(-1)·(-610)
Δ = 113160
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:

$\sqrt{\Delta}=\sqrt{113160}=\sqrt{4*28290}=\sqrt{4}*\sqrt{28290}=2\sqrt{28290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-2\sqrt{28290}}{2*-1}=\frac{-340-2\sqrt{28290}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+2\sqrt{28290}}{2*-1}=\frac{-340+2\sqrt{28290}}{-2}
$