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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(6y+1)/8y^2+4y/8y^2-3=0

We multiply all the terms by the denominator


(6y+1)+4y-3*8y^2=0

We add all the numbers together, and all the variables

4y+(6y+1)-3*8y^2=0

Wy multiply elements

-24y^2+4y+(6y+1)=0

We get rid of parentheses

-24y^2+4y+6y+1=0

We add all the numbers together, and all the variables

-24y^2+10y+1=0

a = -24; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-24)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-24}=\frac{-24}{-48}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-24}=\frac{4}{-48}
=-1/12
$