x=(50+5x)(140-10x)

Solution for x=(50+5x)(140-10x) equation:

x=(50+5x)(140-10x)

We move all terms to the left:

x-((50+5x)(140-10x))=0

We add all the numbers together, and all the variables

x-((5x+50)(-10x+140))=0

We multiply parentheses ..

-((-50x^2+700x-500x+7000))+x=0


We calculate terms in parentheses: -((-50x^2+700x-500x+7000)), so:

(-50x^2+700x-500x+7000)

We get rid of parentheses

-50x^2+700x-500x+7000

We add all the numbers together, and all the variables

-50x^2+200x+7000

Back to the equation:

-(-50x^2+200x+7000)


We get rid of parentheses

50x^2-200x+x-7000=0

We add all the numbers together, and all the variables

50x^2-199x-7000=0

a = 50; b = -199; c = -7000;
Δ = b2-4ac
Δ = -1992-4·50·(-7000)
Δ = 1439601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-\sqrt{1439601}}{2*50}=\frac{199-\sqrt{1439601}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+\sqrt{1439601}}{2*50}=\frac{199+\sqrt{1439601}}{100}
$