x^2-5000x-150000=0

Solution for x^2-5000x-150000=0 equation:

x^2-5000x-150000=0

a = 1; b = -5000; c = -150000;
Δ = b2-4ac
Δ = -50002-4·1·(-150000)
Δ = 25600000
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:

$\sqrt{\Delta}=\sqrt{25600000}=\sqrt{2560000*10}=\sqrt{2560000}*\sqrt{10}=1600\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-1600\sqrt{10}}{2*1}=\frac{5000-1600\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+1600\sqrt{10}}{2*1}=\frac{5000+1600\sqrt{10}}{2}
$