5/4y+6-1/3y=8

Solution for 5/4y+6-1/3y=8 equation:

5/4y+6-1/3y=8

We move all terms to the left:

5/4y+6-1/3y-(8)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

5/4y-1/3y-2=0

We calculate fractions


15y/12y^2+(-4y)/12y^2-2=0

We multiply all the terms by the denominator


15y+(-4y)-2*12y^2=0

Wy multiply elements

-24y^2+15y+(-4y)=0

We get rid of parentheses

-24y^2+15y-4y=0

We add all the numbers together, and all the variables

-24y^2+11y=0

a = -24; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-24)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-24}=\frac{-22}{-48}
=11/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-24}=\frac{0}{-48}
=0
$