13/a+5=5/2a+13

Solution for 13/a+5=5/2a+13 equation:

13/a+5=5/2a+13

We move all terms to the left:

13/a+5-(5/2a+13)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a+13)!=0

a∈R


We get rid of parentheses

13/a-5/2a-13+5=0

We calculate fractions


26a/2a^2+(-5a)/2a^2-13+5=0

We add all the numbers together, and all the variables

26a/2a^2+(-5a)/2a^2-8=0

We multiply all the terms by the denominator


26a+(-5a)-8*2a^2=0

Wy multiply elements

-16a^2+26a+(-5a)=0

We get rid of parentheses

-16a^2+26a-5a=0

We add all the numbers together, and all the variables

-16a^2+21a=0

a = -16; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-16)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-16}=\frac{-42}{-32}
=1+5/16
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-16}=\frac{0}{-32}
=0
$