(3x+8)(x)=240

Solution for (3x+8)(x)=240 equation:

(3x+8)(x)=240

We move all terms to the left:

(3x+8)(x)-(240)=0

We multiply parentheses

3x^2+8x-240=0

a = 3; b = 8; c = -240;
Δ = b2-4ac
Δ = 82-4·3·(-240)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{46}}{2*3}=\frac{-8-8\sqrt{46}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{46}}{2*3}=\frac{-8+8\sqrt{46}}{6}
$