1/5a+a=9

Solution for 1/5a+a=9 equation:

1/5a+a=9

We move all terms to the left:

1/5a+a-(9)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

a+1/5a-9=0

We multiply all the terms by the denominator


a*5a-9*5a+1=0

Wy multiply elements

5a^2-45a+1=0

a = 5; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·5·1
Δ = 2005
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{-(-45)-\sqrt{2005}}{2*5}=\frac{45-\sqrt{2005}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2005}}{2*5}=\frac{45+\sqrt{2005}}{10}
$