26=w-2/3w

Solution for 26=w-2/3w equation:

26=w-2/3w

We move all terms to the left:

26-(w-2/3w)=0


Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-(+w-2/3w)+26=0

We get rid of parentheses

-w+2/3w+26=0

We multiply all the terms by the denominator


-w*3w+26*3w+2=0

Wy multiply elements

-3w^2+78w+2=0

a = -3; b = 78; c = +2;
Δ = b2-4ac
Δ = 782-4·(-3)·2
Δ = 6108
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:

$\sqrt{\Delta}=\sqrt{6108}=\sqrt{4*1527}=\sqrt{4}*\sqrt{1527}=2\sqrt{1527}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1527}}{2*-3}=\frac{-78-2\sqrt{1527}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1527}}{2*-3}=\frac{-78+2\sqrt{1527}}{-6}
$