(350-10x)(20x+150)=25000

Solution for (350-10x)(20x+150)=25000 equation:

(350-10x)(20x+150)=25000

We move all terms to the left:

(350-10x)(20x+150)-(25000)=0

We add all the numbers together, and all the variables

(-10x+350)(20x+150)-25000=0

We multiply parentheses ..

(-200x^2-1500x+7000x+52500)-25000=0

We get rid of parentheses

-200x^2-1500x+7000x+52500-25000=0

We add all the numbers together, and all the variables

-200x^2+5500x+27500=0

a = -200; b = 5500; c = +27500;
Δ = b2-4ac
Δ = 55002-4·(-200)·27500
Δ = 52250000
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:

$\sqrt{\Delta}=\sqrt{52250000}=\sqrt{250000*209}=\sqrt{250000}*\sqrt{209}=500\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5500)-500\sqrt{209}}{2*-200}=\frac{-5500-500\sqrt{209}}{-400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5500)+500\sqrt{209}}{2*-200}=\frac{-5500+500\sqrt{209}}{-400}
$