8a-2=12/a

Solution for 8a-2=12/a equation:

8a-2=12/a

We move all terms to the left:

8a-2-(12/a)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

8a-(+12/a)-2=0

We get rid of parentheses

8a-12/a-2=0

We multiply all the terms by the denominator


8a*a-2*a-12=0

We add all the numbers together, and all the variables

-2a+8a*a-12=0

Wy multiply elements

8a^2-2a-12=0

a = 8; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·8·(-12)
Δ = 388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{97}}{2*8}=\frac{2-2\sqrt{97}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{97}}{2*8}=\frac{2+2\sqrt{97}}{16}
$