7/4a-3=2+9/2a

Solution for 7/4a-3=2+9/2a equation:

7/4a-3=2+9/2a

We move all terms to the left:

7/4a-3-(2+9/2a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

7/4a-(9/2a+2)-3=0

We get rid of parentheses

7/4a-9/2a-2-3=0

We calculate fractions


14a/8a^2+(-36a)/8a^2-2-3=0

We add all the numbers together, and all the variables

14a/8a^2+(-36a)/8a^2-5=0

We multiply all the terms by the denominator


14a+(-36a)-5*8a^2=0

Wy multiply elements

-40a^2+14a+(-36a)=0

We get rid of parentheses

-40a^2+14a-36a=0

We add all the numbers together, and all the variables

-40a^2-22a=0

a = -40; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-40)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-40}=\frac{0}{-80}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-40}=\frac{44}{-80}
=-11/20
$