3/4y-2=-7/8y+3

Solution for 3/4y-2=-7/8y+3 equation:

3/4y-2=-7/8y+3

We move all terms to the left:

3/4y-2-(-7/8y+3)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y+3)!=0

y∈R


We get rid of parentheses

3/4y+7/8y-3-2=0

We calculate fractions


24y/32y^2+28y/32y^2-3-2=0

We add all the numbers together, and all the variables

24y/32y^2+28y/32y^2-5=0

We multiply all the terms by the denominator


24y+28y-5*32y^2=0

We add all the numbers together, and all the variables

52y-5*32y^2=0

Wy multiply elements

-160y^2+52y=0

a = -160; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-160)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-160}=\frac{-104}{-320}
=13/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-160}=\frac{0}{-320}
=0
$