x^2-150x+10,000=0

Solution for x^2-150x+10,000=0 equation:

x^2-150x+10.000=0

We add all the numbers together, and all the variables

x^2-150x+10=0

a = 1; b = -150; c = +10;
Δ = b2-4ac
Δ = -1502-4·1·10
Δ = 22460
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:

$\sqrt{\Delta}=\sqrt{22460}=\sqrt{4*5615}=\sqrt{4}*\sqrt{5615}=2\sqrt{5615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5615}}{2*1}=\frac{150-2\sqrt{5615}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5615}}{2*1}=\frac{150+2\sqrt{5615}}{2}
$