2w^2=-7w-6

Solution for 2w^2=-7w-6 equation:

2w^2=-7w-6

We move all terms to the left:

2w^2-(-7w-6)=0

We get rid of parentheses

2w^2+7w+6=0

a = 2; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·2·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*2}=\frac{-8}{4}
=-2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*2}=\frac{-6}{4}
=-1+1/2
$