3/4y+5/2y=1

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

3/4y+5/2y=1

We move all terms to the left:

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


6y/8y^2+20y/8y^2-1=0

We multiply all the terms by the denominator


6y+20y-1*8y^2=0

We add all the numbers together, and all the variables

26y-1*8y^2=0

Wy multiply elements

-8y^2+26y=0

a = -8; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-8)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-8}=\frac{-52}{-16}
=3+1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-8}=\frac{0}{-16}
=0
$