15w/9w-12=4+15w/4+3w

Solution for 15w/9w-12=4+15w/4+3w equation:

15w/9w-12=4+15w/4+3w

We move all terms to the left:

15w/9w-12-(4+15w/4+3w)=0


Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R



Domain of the equation: 4+3w)!=0

We move all terms containing w to the left, all other terms to the right

3w)!=-4

w!=-4/1

w!=-4

w∈R


We add all the numbers together, and all the variables

15w/9w-(3w+15w/4+4)-12=0

We get rid of parentheses

15w/9w-3w-15w/4-4-12=0

We calculate fractions


(-135w^2)/36w-3w+60w/36w-4-12=0

We add all the numbers together, and all the variables

(-135w^2)/36w-3w+60w/36w-16=0

We multiply all the terms by the denominator


(-135w^2)-3w*36w+60w-16*36w=0

We add all the numbers together, and all the variables

(-135w^2)+60w-3w*36w-16*36w=0

Wy multiply elements

(-135w^2)-108w^2+60w-576w=0

We get rid of parentheses

-135w^2-108w^2+60w-576w=0

We add all the numbers together, and all the variables

-243w^2-516w=0

a = -243; b = -516; c = 0;
Δ = b2-4ac
Δ = -5162-4·(-243)·0
Δ = 266256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{266256}=516$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-516)-516}{2*-243}=\frac{0}{-486}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-516)+516}{2*-243}=\frac{1032}{-486}
=-2+10/81
$