-4+w+7-2/3w=16

Solution for -4+w+7-2/3w=16 equation:

-4+w+7-2/3w=16

We move all terms to the left:

-4+w+7-2/3w-(16)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

w-2/3w-13=0

We multiply all the terms by the denominator


w*3w-13*3w-2=0

Wy multiply elements

3w^2-39w-2=0

a = 3; b = -39; c = -2;
Δ = b2-4ac
Δ = -392-4·3·(-2)
Δ = 1545
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{-(-39)-\sqrt{1545}}{2*3}=\frac{39-\sqrt{1545}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1545}}{2*3}=\frac{39+\sqrt{1545}}{6}
$