8/4y+10/2y=30

Solution for 8/4y+10/2y=30 equation:

8/4y+10/2y=30

We move all terms to the left:

8/4y+10/2y-(30)=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


16y/8y^2+40y/8y^2-30=0

We multiply all the terms by the denominator


16y+40y-30*8y^2=0

We add all the numbers together, and all the variables

56y-30*8y^2=0

Wy multiply elements

-240y^2+56y=0

a = -240; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-240)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-240}=\frac{-112}{-480}
=7/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-240}=\frac{0}{-480}
=0
$