x^2-100x+750=0

Solution for x^2-100x+750=0 equation:

x^2-100x+750=0

a = 1; b = -100; c = +750;
Δ = b2-4ac
Δ = -1002-4·1·750
Δ = 7000
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:

$\sqrt{\Delta}=\sqrt{7000}=\sqrt{100*70}=\sqrt{100}*\sqrt{70}=10\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{70}}{2*1}=\frac{100-10\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{70}}{2*1}=\frac{100+10\sqrt{70}}{2}
$