5/8a-6=3/4a

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

5/8a-6=3/4a

We move all terms to the left:

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


Domain of the equation: 8a!=0

a!=0/8

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

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-192a^2+20a-24a=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{0}{-384}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-192}=\frac{8}{-384}
=-1/48
$