2/a-3/4a=2

Solution for 2/a-3/4a=2 equation:

2/a-3/4a=2

We move all terms to the left:

2/a-3/4a-(2)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We calculate fractions


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

We multiply all the terms by the denominator


8a+(-3a)-2*4a^2=0

Wy multiply elements

-8a^2+8a+(-3a)=0

We get rid of parentheses

-8a^2+8a-3a=0

We add all the numbers together, and all the variables

-8a^2+5a=0

a = -8; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-8)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-8}=\frac{-10}{-16}
=5/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-8}=\frac{0}{-16}
=0
$