(-10x+150)(20x+150)=25000

Solution for (-10x+150)(20x+150)=25000 equation:

(-10x+150)(20x+150)=25000

We move all terms to the left:

(-10x+150)(20x+150)-(25000)=0

We multiply parentheses ..

(-200x^2-1500x+3000x+22500)-25000=0

We get rid of parentheses

-200x^2-1500x+3000x+22500-25000=0

We add all the numbers together, and all the variables

-200x^2+1500x-2500=0

a = -200; b = 1500; c = -2500;
Δ = b2-4ac
Δ = 15002-4·(-200)·(-2500)
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-500}{2*-200}=\frac{-2000}{-400}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+500}{2*-200}=\frac{-1000}{-400}
=2+1/2
$