19/4-7/2a=-1/4a+3-

Solution for 19/4-7/2a=-1/4a+3- equation:

19/4-7/2a=-1/4a+3-

We move all terms to the left:

19/4-7/2a-(-1/4a+3-)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a+3-)!=0

We move all terms containing a to the left, all other terms to the right

4a-)!=-3

a∈R


We add all the numbers together, and all the variables

-7/2a-(-1/4a)+19/4=0

We get rid of parentheses

-7/2a+1/4a+19/4=0

We calculate fractions


608a^2/128a^2+(-448a)/128a^2+32a/128a^2=0

We multiply all the terms by the denominator


608a^2+(-448a)+32a=0

We add all the numbers together, and all the variables

608a^2+32a+(-448a)=0

We get rid of parentheses

608a^2+32a-448a=0

We add all the numbers together, and all the variables

608a^2-416a=0

a = 608; b = -416; c = 0;
Δ = b2-4ac
Δ = -4162-4·608·0
Δ = 173056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173056}=416$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-416)-416}{2*608}=\frac{0}{1216}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-416)+416}{2*608}=\frac{832}{1216}
=13/19
$