2/3y+5/6y=3/4

Solution for 2/3y+5/6y=3/4 equation:

2/3y+5/6y=3/4

We move all terms to the left:

2/3y+5/6y-(3/4)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y+5/6y-(+3/4)=0

We get rid of parentheses

2/3y+5/6y-3/4=0

We calculate fractions


(-324y^2)/288y^2+192y/288y^2+240y/288y^2=0

We multiply all the terms by the denominator


(-324y^2)+192y+240y=0

We add all the numbers together, and all the variables

(-324y^2)+432y=0

We get rid of parentheses

-324y^2+432y=0

a = -324; b = 432; c = 0;
Δ = b2-4ac
Δ = 4322-4·(-324)·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(432)-432}{2*-324}=\frac{-864}{-648}
=1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(432)+432}{2*-324}=\frac{0}{-648}
=0
$