3y+5/16y=2

Solution for 3y+5/16y=2 equation:

3y+5/16y=2

We move all terms to the left:

3y+5/16y-(2)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R


We multiply all the terms by the denominator


3y*16y-2*16y+5=0

Wy multiply elements

48y^2-32y+5=0

a = 48; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·48·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8}{2*48}=\frac{24}{96}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8}{2*48}=\frac{40}{96}
=5/12
$