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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a-12)!=0

a∈R


We get rid of parentheses

1/2a-1/4a+12+4=0

We calculate fractions


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

We add all the numbers together, and all the variables

4a/8a^2+(-2a)/8a^2+16=0

We multiply all the terms by the denominator


4a+(-2a)+16*8a^2=0

Wy multiply elements

128a^2+4a+(-2a)=0

We get rid of parentheses

128a^2+4a-2a=0

We add all the numbers together, and all the variables

128a^2+2a=0

a = 128; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·128·0
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*128}=\frac{-4}{256}
=-1/64
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*128}=\frac{0}{256}
=0
$