2w2+11w=12

Solution for 2w2+11w=12 equation:

2w^2+11w=12

We move all terms to the left:

2w^2+11w-(12)=0

a = 2; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·2·(-12)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{217}}{2*2}=\frac{-11-\sqrt{217}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*2}=\frac{-11+\sqrt{217}}{4}
$