6/a-3-3/8=21/4a-12

Solution for 6/a-3-3/8=21/4a-12 equation:

6/a-3-3/8=21/4a-12

We move all terms to the left:

6/a-3-3/8-(21/4a-12)=0


Domain of the equation: a!=0

a∈R



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

a∈R


We get rid of parentheses

6/a-21/4a+12-3-3/8=0

We calculate fractions


(-48a^2)/256a^2+1536a/256a^2+(-1344a)/256a^2+12-3=0

We add all the numbers together, and all the variables

(-48a^2)/256a^2+1536a/256a^2+(-1344a)/256a^2+9=0

We multiply all the terms by the denominator


(-48a^2)+1536a+(-1344a)+9*256a^2=0

Wy multiply elements

(-48a^2)+2304a^2+1536a+(-1344a)=0

We get rid of parentheses

-48a^2+2304a^2+1536a-1344a=0

We add all the numbers together, and all the variables

2256a^2+192a=0

a = 2256; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·2256·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*2256}=\frac{-384}{4512}
=-4/47
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*2256}=\frac{0}{4512}
=0
$