0=(x-6)(250-5x)

Solution for 0=(x-6)(250-5x) equation:

0=(x-6)(250-5x)

We move all terms to the left:

0-((x-6)(250-5x))=0

We add all the numbers together, and all the variables

-((x-6)(-5x+250))+0=0

We add all the numbers together, and all the variables

-((x-6)(-5x+250))=0

We multiply parentheses ..

-((-5x^2+250x+30x-1500))=0


We calculate terms in parentheses: -((-5x^2+250x+30x-1500)), so:

(-5x^2+250x+30x-1500)

We get rid of parentheses

-5x^2+250x+30x-1500

We add all the numbers together, and all the variables

-5x^2+280x-1500

Back to the equation:

-(-5x^2+280x-1500)


We get rid of parentheses

5x^2-280x+1500=0

a = 5; b = -280; c = +1500;
Δ = b2-4ac
Δ = -2802-4·5·1500
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-220}{2*5}=\frac{60}{10}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+220}{2*5}=\frac{500}{10}
=50
$