-4w2-7w=3w2-6

Solution for -4w2-7w=3w2-6 equation:

-4w^2-7w=3w^2-6

We move all terms to the left:

-4w^2-7w-(3w^2-6)=0

We get rid of parentheses

-4w^2-3w^2-7w+6=0

We add all the numbers together, and all the variables

-7w^2-7w+6=0

a = -7; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-7)·6
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{-(-7)-\sqrt{217}}{2*-7}=\frac{7-\sqrt{217}}{-14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*-7}=\frac{7+\sqrt{217}}{-14}
$