2a-7/4+7=a/3a=

Solution for 2a-7/4+7=a/3a= equation:

2a-7/4+7=a/3a=

We move all terms to the left:

2a-7/4+7-(a/3a)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a-(+a/3a)+7-7/4=0

We get rid of parentheses

2a-a/3a+7-7/4=0

We calculate fractions


2a+(-4a)/12a+(-21a)/12a+7=0

We multiply all the terms by the denominator


2a*12a+(-4a)+(-21a)+7*12a=0

Wy multiply elements

24a^2+(-4a)+(-21a)+84a=0

We get rid of parentheses

24a^2-4a-21a+84a=0

We add all the numbers together, and all the variables

24a^2+59a=0

a = 24; b = 59; c = 0;
Δ = b2-4ac
Δ = 592-4·24·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-59}{2*24}=\frac{-118}{48}
=-2+11/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+59}{2*24}=\frac{0}{48}
=0
$