x2-60x+750=0

Solution for x2-60x+750=0 equation:

x2-60x+750=0

We add all the numbers together, and all the variables

x^2-60x+750=0

a = 1; b = -60; c = +750;
Δ = b2-4ac
Δ = -602-4·1·750
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{6}}{2*1}=\frac{60-10\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{6}}{2*1}=\frac{60+10\sqrt{6}}{2}
$