2/3y+3/4y=34

Solution for 2/3y+3/4y=34 equation:

2/3y+3/4y=34

We move all terms to the left:

2/3y+3/4y-(34)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


8y/12y^2+9y/12y^2-34=0

We multiply all the terms by the denominator


8y+9y-34*12y^2=0

We add all the numbers together, and all the variables

17y-34*12y^2=0

Wy multiply elements

-408y^2+17y=0

a = -408; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-408)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-408}=\frac{-34}{-816}
=1/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-408}=\frac{0}{-816}
=0
$