3/7w+5/2w=1

Solution for 3/7w+5/2w=1 equation:

3/7w+5/2w=1

We move all terms to the left:

3/7w+5/2w-(1)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We calculate fractions


6w/14w^2+35w/14w^2-1=0

We multiply all the terms by the denominator


6w+35w-1*14w^2=0

We add all the numbers together, and all the variables

41w-1*14w^2=0

Wy multiply elements

-14w^2+41w=0

a = -14; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-14)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-14}=\frac{-82}{-28}
=2+13/14
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-14}=\frac{0}{-28}
=0
$