0=(90+10x)(250-5x)

Solution for 0=(90+10x)(250-5x) equation:

0=(90+10x)(250-5x)

We move all terms to the left:

0-((90+10x)(250-5x))=0

We add all the numbers together, and all the variables

-((10x+90)(-5x+250))+0=0

We add all the numbers together, and all the variables

-((10x+90)(-5x+250))=0

We multiply parentheses ..

-((-50x^2+2500x-450x+22500))=0


We calculate terms in parentheses: -((-50x^2+2500x-450x+22500)), so:

(-50x^2+2500x-450x+22500)

We get rid of parentheses

-50x^2+2500x-450x+22500

We add all the numbers together, and all the variables

-50x^2+2050x+22500

Back to the equation:

-(-50x^2+2050x+22500)


We get rid of parentheses

50x^2-2050x-22500=0

a = 50; b = -2050; c = -22500;
Δ = b2-4ac
Δ = -20502-4·50·(-22500)
Δ = 8702500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8702500}=2950$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2050)-2950}{2*50}=\frac{-900}{100}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2050)+2950}{2*50}=\frac{5000}{100}
=50
$