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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

32y^2+4y+(-6y)=0

We get rid of parentheses

32y^2+4y-6y=0

We add all the numbers together, and all the variables

32y^2-2y=0

a = 32; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·32·0
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*32}=\frac{0}{64}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*32}=\frac{4}{64}
=1/16
$