100x^2+2500x+1000=15000

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

100x^2+2500x+1000=15000

We move all terms to the left:

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}
$