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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y+2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6y/8y^2+(-4y)/8y^2-7=0

We multiply all the terms by the denominator


6y+(-4y)-7*8y^2=0

Wy multiply elements

-56y^2+6y+(-4y)=0

We get rid of parentheses

-56y^2+6y-4y=0

We add all the numbers together, and all the variables

-56y^2+2y=0

a = -56; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-56)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-56}=\frac{-4}{-112}
=1/28
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-56}=\frac{0}{-112}
=0
$