3a=1/3a+15

Solution for 3a=1/3a+15 equation:

3a=1/3a+15

We move all terms to the left:

3a-(1/3a+15)=0


Domain of the equation: 3a+15)!=0

a∈R


We get rid of parentheses

3a-1/3a-15=0

We multiply all the terms by the denominator


3a*3a-15*3a-1=0

Wy multiply elements

9a^2-45a-1=0

a = 9; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·9·(-1)
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{229}}{2*9}=\frac{45-3\sqrt{229}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{229}}{2*9}=\frac{45+3\sqrt{229}}{18}
$