x^2-150x=10000

Solution for x^2-150x=10000 equation:

x^2-150x=10000

We move all terms to the left:

x^2-150x-(10000)=0

a = 1; b = -150; c = -10000;
Δ = b2-4ac
Δ = -1502-4·1·(-10000)
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-250}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+250}{2*1}=\frac{400}{2}
=200
$