150x+100x(250-80x)=170x+250

Solution for 150x+100x(250-80x)=170x+250 equation:

150x+100x(250-80x)=170x+250

We move all terms to the left:

150x+100x(250-80x)-(170x+250)=0

We add all the numbers together, and all the variables

150x+100x(-80x+250)-(170x+250)=0

We multiply parentheses

-8000x^2+150x+25000x-(170x+250)=0

We get rid of parentheses

-8000x^2+150x+25000x-170x-250=0

We add all the numbers together, and all the variables

-8000x^2+24980x-250=0

a = -8000; b = 24980; c = -250;
Δ = b2-4ac
Δ = 249802-4·(-8000)·(-250)
Δ = 616000400
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:

$\sqrt{\Delta}=\sqrt{616000400}=\sqrt{400*1540001}=\sqrt{400}*\sqrt{1540001}=20\sqrt{1540001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24980)-20\sqrt{1540001}}{2*-8000}=\frac{-24980-20\sqrt{1540001}}{-16000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24980)+20\sqrt{1540001}}{2*-8000}=\frac{-24980+20\sqrt{1540001}}{-16000}
$