15000=100x^2+2500x+1000

Solution for 15000=100x^2+2500x+1000 equation:

15000=100x^2+2500x+1000

We move all terms to the left:

15000-(100x^2+2500x+1000)=0

We get rid of parentheses

-100x^2-2500x-1000+15000=0

We add all the numbers together, and all the variables

-100x^2-2500x+14000=0

a = -100; b = -2500; c = +14000;
Δ = b2-4ac
Δ = -25002-4·(-100)·14000
Δ = 11850000
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:

$\sqrt{\Delta}=\sqrt{11850000}=\sqrt{10000*1185}=\sqrt{10000}*\sqrt{1185}=100\sqrt{1185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-100\sqrt{1185}}{2*-100}=\frac{2500-100\sqrt{1185}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+100\sqrt{1185}}{2*-100}=\frac{2500+100\sqrt{1185}}{-200}
$