5a=3+3/5a

Solution for 5a=3+3/5a equation:

5a=3+3/5a

We move all terms to the left:

5a-(3+3/5a)=0


Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

5a-(3/5a+3)=0

We get rid of parentheses

5a-3/5a-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

25a^2-15a-3=0

a = 25; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·25·(-3)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{21}}{2*25}=\frac{15-5\sqrt{21}}{50}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{21}}{2*25}=\frac{15+5\sqrt{21}}{50}
$