4+4/5a=9/10a

Solution for 4+4/5a=9/10a equation:

4+4/5a=9/10a

We move all terms to the left:

4+4/5a-(9/10a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 10a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

4/5a-(+9/10a)+4=0

We get rid of parentheses

4/5a-9/10a+4=0

We calculate fractions


40a/50a^2+(-45a)/50a^2+4=0

We multiply all the terms by the denominator


40a+(-45a)+4*50a^2=0

Wy multiply elements

200a^2+40a+(-45a)=0

We get rid of parentheses

200a^2+40a-45a=0

We add all the numbers together, and all the variables

200a^2-5a=0

a = 200; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·200·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*200}=\frac{0}{400}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*200}=\frac{10}{400}
=1/40
$