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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4y+2y-7*8y^2=0

We add all the numbers together, and all the variables

6y-7*8y^2=0

Wy multiply elements

-56y^2+6y=0

a = -56; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-56)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-56}=\frac{-12}{-112}
=3/28
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-56}=\frac{0}{-112}
=0
$