3/8a+3/4a+1/2=6

Solution for 3/8a+3/4a+1/2=6 equation:

3/8a+3/4a+1/2=6

We move all terms to the left:

3/8a+3/4a+1/2-(6)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


determiningTheFunctionDomain
3/8a+3/4a-6+1/2=0

We calculate fractions


128a^2/128a^2+48a/128a^2+96a/128a^2-6=0

Fractions to decimals

48a/128a^2+96a/128a^2-6+1=0

We multiply all the terms by the denominator


48a+96a-6*128a^2+1*128a^2=0

We add all the numbers together, and all the variables

144a-6*128a^2+1*128a^2=0

Wy multiply elements

-768a^2+128a^2+144a=0

We add all the numbers together, and all the variables

-640a^2+144a=0

a = -640; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-640)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-640}=\frac{-288}{-1280}
=9/40
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-640}=\frac{0}{-1280}
=0
$