4w^2+2w=240

Solution for 4w^2+2w=240 equation:

4w^2+2w=240

We move all terms to the left:

4w^2+2w-(240)=0

a = 4; b = 2; c = -240;
Δ = b2-4ac
Δ = 22-4·4·(-240)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-62}{2*4}=\frac{-64}{8}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+62}{2*4}=\frac{60}{8}
=7+1/2
$