2a+13=7/a

Solution for 2a+13=7/a equation:

2a+13=7/a

We move all terms to the left:

2a+13-(7/a)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a-(+7/a)+13=0

We get rid of parentheses

2a-7/a+13=0

We multiply all the terms by the denominator


2a*a+13*a-7=0

We add all the numbers together, and all the variables

13a+2a*a-7=0

Wy multiply elements

2a^2+13a-7=0

a = 2; b = 13; c = -7;
Δ = b2-4ac
Δ = 132-4·2·(-7)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-15}{2*2}=\frac{-28}{4}
=-7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+15}{2*2}=\frac{2}{4}
=1/2
$