12-9/16a=3/4a

Solution for 12-9/16a=3/4a equation:

12-9/16a=3/4a

We move all terms to the left:

12-9/16a-(3/4a)=0


Domain of the equation: 16a!=0

a!=0/16

a!=0

a∈R



Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-9/16a-(+3/4a)+12=0

We get rid of parentheses

-9/16a-3/4a+12=0

We calculate fractions


(-36a)/64a^2+(-48a)/64a^2+12=0

We multiply all the terms by the denominator


(-36a)+(-48a)+12*64a^2=0

Wy multiply elements

768a^2+(-36a)+(-48a)=0

We get rid of parentheses

768a^2-36a-48a=0

We add all the numbers together, and all the variables

768a^2-84a=0

a = 768; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·768·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*768}=\frac{0}{1536}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*768}=\frac{168}{1536}
=7/64
$