250=x(0.5x-5)

Solution for 250=x(0.5x-5) equation:

250=x(0.5x-5)

We move all terms to the left:

250-(x(0.5x-5))=0


We calculate terms in parentheses: -(x(0.5x-5)), so:

x(0.5x-5)

We multiply parentheses

0x^2-5x

We add all the numbers together, and all the variables

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

-x^2+5x+250=0

We add all the numbers together, and all the variables

-1x^2+5x+250=0

a = -1; b = 5; c = +250;
Δ = b2-4ac
Δ = 52-4·(-1)·250
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{41}}{2*-1}=\frac{-5-5\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{41}}{2*-1}=\frac{-5+5\sqrt{41}}{-2}
$