1/2a+1/a=14

Solution for 1/2a+1/a=14 equation:

1/2a+1/a=14

We move all terms to the left:

1/2a+1/a-(14)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: a!=0

a∈R


We calculate fractions


a/2a^2+2a/2a^2-14=0

We multiply all the terms by the denominator


a+2a-14*2a^2=0

We add all the numbers together, and all the variables

3a-14*2a^2=0

Wy multiply elements

-28a^2+3a=0

a = -28; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-28)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-28}=\frac{-6}{-56}
=3/28
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-28}=\frac{0}{-56}
=0
$