240=(3x+4)(x)

Solution for 240=(3x+4)(x) equation:

240=(3x+4)(x)

We move all terms to the left:

240-((3x+4)(x))=0


We calculate terms in parentheses: -((3x+4)x), so:

(3x+4)x

We multiply parentheses

3x^2+4x

Back to the equation:

-(3x^2+4x)


We get rid of parentheses

-3x^2-4x+240=0

a = -3; b = -4; c = +240;
Δ = b2-4ac
Δ = -42-4·(-3)·240
Δ = 2896
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:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{181}}{2*-3}=\frac{4-4\sqrt{181}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{181}}{2*-3}=\frac{4+4\sqrt{181}}{-6}
$