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 = 22540
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:

$\sqrt{\Delta}=\sqrt{22540}=\sqrt{196*115}=\sqrt{196}*\sqrt{115}=14\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-14\sqrt{115}}{2*1}=\frac{-150-14\sqrt{115}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+14\sqrt{115}}{2*1}=\frac{-150+14\sqrt{115}}{2}
$