1/5a-1/2a=4+3/2a

Solution for 1/5a-1/2a=4+3/2a equation:

1/5a-1/2a=4+3/2a

We move all terms to the left:

1/5a-1/2a-(4+3/2a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/5a-1/2a-(3/2a+4)=0

We get rid of parentheses

1/5a-1/2a-3/2a-4=0

We calculate fractions


2a/10a^2+(-15a-1)/10a^2-4=0

We multiply all the terms by the denominator


2a+(-15a-1)-4*10a^2=0

Wy multiply elements

-40a^2+2a+(-15a-1)=0

We get rid of parentheses

-40a^2+2a-15a-1=0

We add all the numbers together, and all the variables

-40a^2-13a-1=0

a = -40; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·(-40)·(-1)
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{-(-13)-3}{2*-40}=\frac{10}{-80}
=-1/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*-40}=\frac{16}{-80}
=-1/5
$