a+5=3/5a

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

a+5=3/5a

We move all terms to the left:

a+5-(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

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

We get rid of parentheses

a-3/5a+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

5a^2+25a-3=0

a = 5; b = 25; c = -3;
Δ = b2-4ac
Δ = 252-4·5·(-3)
Δ = 685
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{-(25)-\sqrt{685}}{2*5}=\frac{-25-\sqrt{685}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{685}}{2*5}=\frac{-25+\sqrt{685}}{10}
$