3/4a+6=5/8a

Solution for 3/4a+6=5/8a equation:

3/4a+6=5/8a

We move all terms to the left:

3/4a+6-(5/8a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3/4a-(+5/8a)+6=0

We get rid of parentheses

3/4a-5/8a+6=0

We calculate fractions


24a/32a^2+(-20a)/32a^2+6=0

We multiply all the terms by the denominator


24a+(-20a)+6*32a^2=0

Wy multiply elements

192a^2+24a+(-20a)=0

We get rid of parentheses

192a^2+24a-20a=0

We add all the numbers together, and all the variables

192a^2+4a=0

a = 192; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·192·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*192}=\frac{-8}{384}
=-1/48
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*192}=\frac{0}{384}
=0
$