O.25y=2/y-6

Solution for O.25y=2/y-6 equation:

.25O=2/O-6

We move all terms to the left:

.25O-(2/O-6)=0


Domain of the equation: O-6)!=0

O∈R


We get rid of parentheses

.25O-2/O+6=0

We multiply all the terms by the denominator


(.25O)*O+6*O-2=0

We add all the numbers together, and all the variables

(+.25O)*O+6*O-2=0

We add all the numbers together, and all the variables

6O+(+.25O)*O-2=0

We multiply parentheses

O^2+6O-2=0

a = 1; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·1·(-2)
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*1}=\frac{-6-2\sqrt{11}}{2}
$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*1}=\frac{-6+2\sqrt{11}}{2}
$