125=15x(x-75)+50

Solution for 125=15x(x-75)+50 equation:

125=15x(x-75)+50

We move all terms to the left:

125-(15x(x-75)+50)=0


We calculate terms in parentheses: -(15x(x-75)+50), so:

15x(x-75)+50

We multiply parentheses

15x^2-1125x+50

Back to the equation:

-(15x^2-1125x+50)


We get rid of parentheses

-15x^2+1125x-50+125=0

We add all the numbers together, and all the variables

-15x^2+1125x+75=0

a = -15; b = 1125; c = +75;
Δ = b2-4ac
Δ = 11252-4·(-15)·75
Δ = 1270125
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:

$\sqrt{\Delta}=\sqrt{1270125}=\sqrt{225*5645}=\sqrt{225}*\sqrt{5645}=15\sqrt{5645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1125)-15\sqrt{5645}}{2*-15}=\frac{-1125-15\sqrt{5645}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1125)+15\sqrt{5645}}{2*-15}=\frac{-1125+15\sqrt{5645}}{-30}
$