7/11w+4/w=1

Solution for 7/11w+4/w=1 equation:

7/11w+4/w=1

We move all terms to the left:

7/11w+4/w-(1)=0


Domain of the equation: 11w!=0

w!=0/11

w!=0

w∈R



Domain of the equation: w!=0

w∈R


We calculate fractions


7w/11w^2+44w/11w^2-1=0

We multiply all the terms by the denominator


7w+44w-1*11w^2=0

We add all the numbers together, and all the variables

51w-1*11w^2=0

Wy multiply elements

-11w^2+51w=0

a = -11; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-11)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-11}=\frac{-102}{-22}
=4+7/11
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-11}=\frac{0}{-22}
=0
$