4/9w=w-8

Solution for 4/9w=w-8 equation:

4/9w=w-8

We move all terms to the left:

4/9w-(w-8)=0


Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R


We get rid of parentheses

4/9w-w+8=0

We multiply all the terms by the denominator


-w*9w+8*9w+4=0

Wy multiply elements

-9w^2+72w+4=0

a = -9; b = 72; c = +4;
Δ = b2-4ac
Δ = 722-4·(-9)·4
Δ = 5328
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:

$\sqrt{\Delta}=\sqrt{5328}=\sqrt{144*37}=\sqrt{144}*\sqrt{37}=12\sqrt{37}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{37}}{2*-9}=\frac{-72-12\sqrt{37}}{-18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{37}}{2*-9}=\frac{-72+12\sqrt{37}}{-18}
$