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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a+2)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-48a^2+4a+(-6a)=0

We get rid of parentheses

-48a^2+4a-6a=0

We add all the numbers together, and all the variables

-48a^2-2a=0

a = -48; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-48)·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*-48}=\frac{0}{-96}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-48}=\frac{4}{-96}
=-1/24
$