6y+8/y-2=24

Solution for 6y+8/y-2=24 equation:

6y+8/y-2=24

We move all terms to the left:

6y+8/y-2-(24)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

6y+8/y-26=0

We multiply all the terms by the denominator


6y*y-26*y+8=0

We add all the numbers together, and all the variables

-26y+6y*y+8=0

Wy multiply elements

6y^2-26y+8=0

a = 6; b = -26; c = +8;
Δ = b2-4ac
Δ = -262-4·6·8
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*6}=\frac{4}{12}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*6}=\frac{48}{12}
=4
$