3/4a-3=a

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

3/4a-3=a

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4a^2-12a+3=0

a = -4; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-4)·3
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*-4}=\frac{12-8\sqrt{3}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*-4}=\frac{12+8\sqrt{3}}{-8}
$