x(2x+5)=250

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

x(2x+5)=250

We move all terms to the left:

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

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