1/2a-4=3/4a

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

1/2a-4=3/4a

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4a/8a^2+(-6a)/8a^2-4=0

We multiply all the terms by the denominator


4a+(-6a)-4*8a^2=0

Wy multiply elements

-32a^2+4a+(-6a)=0

We get rid of parentheses

-32a^2+4a-6a=0

We add all the numbers together, and all the variables

-32a^2-2a=0

a = -32; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-32)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-32}=\frac{0}{-64}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-32}=\frac{4}{-64}
=-1/16
$