250=x(2x+5)

Solution for 250=x(2x+5) equation:

250=x(2x+5)

We move all terms to the left:

250-(x(2x+5))=0


We calculate terms in parentheses: -(x(2x+5)), so:

x(2x+5)

We multiply parentheses

2x^2+5x

Back to the equation:

-(2x^2+5x)


We get rid of parentheses

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

a = -2; b = -5; c = +250;
Δ = b2-4ac
Δ = -52-4·(-2)·250
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*-2}=\frac{50}{-4}
=-12+1/2
$