32x+2x^2=240

Solution for 32x+2x^2=240 equation:

32x+2x^2=240

We move all terms to the left:

32x+2x^2-(240)=0

a = 2; b = 32; c = -240;
Δ = b2-4ac
Δ = 322-4·2·(-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{-(32)-8\sqrt{46}}{2*2}=\frac{-32-8\sqrt{46}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{46}}{2*2}=\frac{-32+8\sqrt{46}}{4}
$