1/2a-12=5/4a+6

Solution for 1/2a-12=5/4a+6 equation:

1/2a-12=5/4a+6

We move all terms to the left:

1/2a-12-(5/4a+6)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a+6)!=0

a∈R


We get rid of parentheses

1/2a-5/4a-6-12=0

We calculate fractions


4a/8a^2+(-10a)/8a^2-6-12=0

We add all the numbers together, and all the variables

4a/8a^2+(-10a)/8a^2-18=0

We multiply all the terms by the denominator


4a+(-10a)-18*8a^2=0

Wy multiply elements

-144a^2+4a+(-10a)=0

We get rid of parentheses

-144a^2+4a-10a=0

We add all the numbers together, and all the variables

-144a^2-6a=0

a = -144; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-144)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-144}=\frac{0}{-288}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-144}=\frac{12}{-288}
=-1/24
$