260=x(2x+9)

Solution for 260=x(2x+9) equation:

260=x(2x+9)

We move all terms to the left:

260-(x(2x+9))=0


We calculate terms in parentheses: -(x(2x+9)), so:

x(2x+9)

We multiply parentheses

2x^2+9x

Back to the equation:

-(2x^2+9x)


We get rid of parentheses

-2x^2-9x+260=0

a = -2; b = -9; c = +260;
Δ = b2-4ac
Δ = -92-4·(-2)·260
Δ = 2161
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{-(-9)-\sqrt{2161}}{2*-2}=\frac{9-\sqrt{2161}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{2161}}{2*-2}=\frac{9+\sqrt{2161}}{-4}
$