3/2y+1/4y=30

Solution for 3/2y+1/4y=30 equation:

3/2y+1/4y=30

We move all terms to the left:

3/2y+1/4y-(30)=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 calculate fractions


12y/8y^2+2y/8y^2-30=0

We multiply all the terms by the denominator


12y+2y-30*8y^2=0

We add all the numbers together, and all the variables

14y-30*8y^2=0

Wy multiply elements

-240y^2+14y=0

a = -240; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-240)·0
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{-(14)-14}{2*-240}=\frac{-28}{-480}
=7/120
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-240}=\frac{0}{-480}
=0
$