19/4a-2/a=1

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

19/4a-2/a=1

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: a!=0

a∈R


We calculate fractions


19a/4a^2+(-8a)/4a^2-1=0

We multiply all the terms by the denominator


19a+(-8a)-1*4a^2=0

Wy multiply elements

-4a^2+19a+(-8a)=0

We get rid of parentheses

-4a^2+19a-8a=0

We add all the numbers together, and all the variables

-4a^2+11a=0

a = -4; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-4)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-4}=\frac{-22}{-8}
=2+3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-4}=\frac{0}{-8}
=0
$