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

Solution for 1/2y-3=5-3/4y equation:

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(-3/4y+5)-3=0

We get rid of parentheses

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

We calculate fractions


4y/8y^2+6y/8y^2-5-3=0

We add all the numbers together, and all the variables

4y/8y^2+6y/8y^2-8=0

We multiply all the terms by the denominator


4y+6y-8*8y^2=0

We add all the numbers together, and all the variables

10y-8*8y^2=0

Wy multiply elements

-64y^2+10y=0

a = -64; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-64)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-64}=\frac{-20}{-128}
=5/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-64}=\frac{0}{-128}
=0
$