250=3x(x+1)

Solution for 250=3x(x+1) equation:

250=3x(x+1)

We move all terms to the left:

250-(3x(x+1))=0


We calculate terms in parentheses: -(3x(x+1)), so:

3x(x+1)

We multiply parentheses

3x^2+3x

Back to the equation:

-(3x^2+3x)


We get rid of parentheses

-3x^2-3x+250=0

a = -3; b = -3; c = +250;
Δ = b2-4ac
Δ = -32-4·(-3)·250
Δ = 3009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{3009}}{2*-3}=\frac{3-\sqrt{3009}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{3009}}{2*-3}=\frac{3+\sqrt{3009}}{-6}
$