2/a+3/4=5/6a

Solution for 2/a+3/4=5/6a equation:

2/a+3/4=5/6a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 6a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


108a^2/96a^2+192a/96a^2+(-80a)/96a^2=0

We multiply all the terms by the denominator


108a^2+192a+(-80a)=0

We get rid of parentheses

108a^2+192a-80a=0

We add all the numbers together, and all the variables

108a^2+112a=0

a = 108; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·108·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*108}=\frac{-224}{216}
=-1+1/27
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*108}=\frac{0}{216}
=0
$