3/72w-11=-4/7w

Solution for 3/72w-11=-4/7w equation:

3/72w-11=-4/7w

We move all terms to the left:

3/72w-11-(-4/7w)=0


Domain of the equation: 72w!=0

w!=0/72

w!=0

w∈R



Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3/72w+4/7w-11=0

We calculate fractions


21w/504w^2+288w/504w^2-11=0

We multiply all the terms by the denominator


21w+288w-11*504w^2=0

We add all the numbers together, and all the variables

309w-11*504w^2=0

Wy multiply elements

-5544w^2+309w=0

a = -5544; b = 309; c = 0;
Δ = b2-4ac
Δ = 3092-4·(-5544)·0
Δ = 95481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{95481}=309$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(309)-309}{2*-5544}=\frac{-618}{-11088}
=103/1848
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(309)+309}{2*-5544}=\frac{0}{-11088}
=0
$