14=y+48/y

Solution for 14=y+48/y equation:

14=y+48/y

We move all terms to the left:

14-(y+48/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(+y+48/y)+14=0

We get rid of parentheses

-y-48/y+14=0

We multiply all the terms by the denominator


-y*y+14*y-48=0

We add all the numbers together, and all the variables

14y-y*y-48=0

Wy multiply elements

-1y^2+14y-48=0

a = -1; b = 14; c = -48;
Δ = b2-4ac
Δ = 142-4·(-1)·(-48)
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{-(14)-2}{2*-1}=\frac{-16}{-2}
=+8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-1}=\frac{-12}{-2}
=+6
$