w=4/6w+4

Solution for w=4/6w+4 equation:

w=4/6w+4

We move all terms to the left:

w-(4/6w+4)=0


Domain of the equation: 6w+4)!=0

w∈R


We get rid of parentheses

w-4/6w-4=0

We multiply all the terms by the denominator


w*6w-4*6w-4=0

Wy multiply elements

6w^2-24w-4=0

a = 6; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·6·(-4)
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{42}}{2*6}=\frac{24-4\sqrt{42}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{42}}{2*6}=\frac{24+4\sqrt{42}}{12}
$