100=10x(x-70)+50

Solution for 100=10x(x-70)+50 equation:

100=10x(x-70)+50

We move all terms to the left:

100-(10x(x-70)+50)=0


We calculate terms in parentheses: -(10x(x-70)+50), so:

10x(x-70)+50

We multiply parentheses

10x^2-700x+50

Back to the equation:

-(10x^2-700x+50)


We get rid of parentheses

-10x^2+700x-50+100=0

We add all the numbers together, and all the variables

-10x^2+700x+50=0

a = -10; b = 700; c = +50;
Δ = b2-4ac
Δ = 7002-4·(-10)·50
Δ = 492000
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:

$\sqrt{\Delta}=\sqrt{492000}=\sqrt{400*1230}=\sqrt{400}*\sqrt{1230}=20\sqrt{1230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-20\sqrt{1230}}{2*-10}=\frac{-700-20\sqrt{1230}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+20\sqrt{1230}}{2*-10}=\frac{-700+20\sqrt{1230}}{-20}
$