5/2w+7/3w=1

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

5/2w+7/3w=1

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We calculate fractions


15w/6w^2+14w/6w^2-1=0

We multiply all the terms by the denominator


15w+14w-1*6w^2=0

We add all the numbers together, and all the variables

29w-1*6w^2=0

Wy multiply elements

-6w^2+29w=0

a = -6; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-6)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-6}=\frac{-58}{-12}
=4+5/6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-6}=\frac{0}{-12}
=0
$