y+6/y=19

Solution for y+6/y=19 equation:

y+6/y=19

We move all terms to the left:

y+6/y-(19)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


y*y-19*y+6=0

We add all the numbers together, and all the variables

-19y+y*y+6=0

Wy multiply elements

y^2-19y+6=0

a = 1; b = -19; c = +6;
Δ = b2-4ac
Δ = -192-4·1·6
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{337}}{2*1}=\frac{19-\sqrt{337}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{337}}{2*1}=\frac{19+\sqrt{337}}{2}
$