3/4y-7/4y+5=5-y

Solution for 3/4y-7/4y+5=5-y equation:

3/4y-7/4y+5=5-y

We move all terms to the left:

3/4y-7/4y+5-(5-y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-7/4y-(-1y+5)+5=0

We get rid of parentheses

3/4y-7/4y+1y-5+5=0

We multiply all the terms by the denominator


1y*4y-5*4y+5*4y+3-7=0

We add all the numbers together, and all the variables

1y*4y-5*4y+5*4y-4=0

Wy multiply elements

4y^2-20y+20y-4=0

We add all the numbers together, and all the variables

4y^2-4=0

a = 4; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·4·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*4}=\frac{-8}{8}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*4}=\frac{8}{8}
=1
$