1/2a-4=5+1/5a

Solution for 1/2a-4=5+1/5a equation:

1/2a-4=5+1/5a

We move all terms to the left:

1/2a-4-(5+1/5a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/2a-(1/5a+5)-4=0

We get rid of parentheses

1/2a-1/5a-5-4=0

We calculate fractions


5a/10a^2+(-2a)/10a^2-5-4=0

We add all the numbers together, and all the variables

5a/10a^2+(-2a)/10a^2-9=0

We multiply all the terms by the denominator


5a+(-2a)-9*10a^2=0

Wy multiply elements

-90a^2+5a+(-2a)=0

We get rid of parentheses

-90a^2+5a-2a=0

We add all the numbers together, and all the variables

-90a^2+3a=0

a = -90; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-90)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-90}=\frac{-6}{-180}
=1/30
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-90}=\frac{0}{-180}
=0
$