x^2-80x+600=300

Solution for x^2-80x+600=300 equation:

x^2-80x+600=300

We move all terms to the left:

x^2-80x+600-(300)=0

We add all the numbers together, and all the variables

x^2-80x+300=0

a = 1; b = -80; c = +300;
Δ = b2-4ac
Δ = -802-4·1·300
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{13}}{2*1}=\frac{80-20\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{13}}{2*1}=\frac{80+20\sqrt{13}}{2}
$