8=3/4a+12-1a+4

Solution for 8=3/4a+12-1a+4 equation:

8=3/4a+12-1a+4

We move all terms to the left:

8-(3/4a+12-1a+4)=0


Domain of the equation: 4a+12-1a+4)!=0

We move all terms containing a to the left, all other terms to the right

4a-1a+4)!=-12

a∈R


We add all the numbers together, and all the variables

-(-1a+3/4a+16)+8=0

We get rid of parentheses

1a-3/4a-16+8=0

We multiply all the terms by the denominator


1a*4a-16*4a+8*4a-3=0

Wy multiply elements

4a^2-64a+32a-3=0

We add all the numbers together, and all the variables

4a^2-32a-3=0

a = 4; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·4·(-3)
Δ = 1072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{67}}{2*4}=\frac{32-4\sqrt{67}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{67}}{2*4}=\frac{32+4\sqrt{67}}{8}
$