1/2a+a=3/5a+a+5

Solution for 1/2a+a=3/5a+a+5 equation:

1/2a+a=3/5a+a+5

We move all terms to the left:

1/2a+a-(3/5a+a+5)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a+a+5)!=0

a∈R


We add all the numbers together, and all the variables

1/2a+a-(a+3/5a+5)=0

We add all the numbers together, and all the variables

a+1/2a-(a+3/5a+5)=0

We get rid of parentheses

a+1/2a-a-3/5a-5=0

We calculate fractions


a-a+5a/10a^2+(-6a)/10a^2-5=0

We add all the numbers together, and all the variables

5a/10a^2+(-6a)/10a^2-5=0

We multiply all the terms by the denominator


5a+(-6a)-5*10a^2=0

Wy multiply elements

-50a^2+5a+(-6a)=0

We get rid of parentheses

-50a^2+5a-6a=0

We add all the numbers together, and all the variables

-50a^2-1a=0

a = -50; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-50)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-50}=\frac{0}{-100}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-50}=\frac{2}{-100}
=-1/50
$