7/3y+7/8y-3/4=15/8

Solution for 7/3y+7/8y-3/4=15/8 equation:

7/3y+7/8y-3/4=15/8

We move all terms to the left:

7/3y+7/8y-3/4-(15/8)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

7/3y+7/8y-3/4-(+15/8)=0

We get rid of parentheses

7/3y+7/8y-3/4-15/8=0

We calculate fractions


(-4608y^2)/3072y^2+7168y/3072y^2+336y/3072y^2+(-720y)/3072y^2=0

We multiply all the terms by the denominator


(-4608y^2)+7168y+336y+(-720y)=0

We add all the numbers together, and all the variables

(-4608y^2)+7504y+(-720y)=0

We get rid of parentheses

-4608y^2+7504y-720y=0

We add all the numbers together, and all the variables

-4608y^2+6784y=0

a = -4608; b = 6784; c = 0;
Δ = b2-4ac
Δ = 67842-4·(-4608)·0
Δ = 46022656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46022656}=6784$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6784)-6784}{2*-4608}=\frac{-13568}{-9216}
=1+17/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6784)+6784}{2*-4608}=\frac{0}{-9216}
=0
$