3a-1/a+3=8

Solution for 3a-1/a+3=8 equation:

3a-1/a+3=8

We move all terms to the left:

3a-1/a+3-(8)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

3a-1/a-5=0

We multiply all the terms by the denominator


3a*a-5*a-1=0

We add all the numbers together, and all the variables

-5a+3a*a-1=0

Wy multiply elements

3a^2-5a-1=0

a = 3; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·3·(-1)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{37}}{2*3}=\frac{5-\sqrt{37}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*3}=\frac{5+\sqrt{37}}{6}
$