19/a-7/2a=5

Solution for 19/a-7/2a=5 equation:

19/a-7/2a=5

We move all terms to the left:

19/a-7/2a-(5)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We calculate fractions


38a/2a^2+(-7a)/2a^2-5=0

We multiply all the terms by the denominator


38a+(-7a)-5*2a^2=0

Wy multiply elements

-10a^2+38a+(-7a)=0

We get rid of parentheses

-10a^2+38a-7a=0

We add all the numbers together, and all the variables

-10a^2+31a=0

a = -10; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-10)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-10}=\frac{-62}{-20}
=3+1/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-10}=\frac{0}{-20}
=0
$