42/a=13-a

Solution for 42/a=13-a equation:

42/a=13-a

We move all terms to the left:

42/a-(13-a)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

42/a-(-1a+13)=0

We get rid of parentheses

42/a+1a-13=0

We multiply all the terms by the denominator


1a*a-13*a+42=0

We add all the numbers together, and all the variables

-13a+1a*a+42=0

Wy multiply elements

a^2-13a+42=0

a = 1; b = -13; c = +42;
Δ = b2-4ac
Δ = -132-4·1·42
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*1}=\frac{12}{2}
=6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*1}=\frac{14}{2}
=7
$