48/a+a=28

Solution for 48/a+a=28 equation:

48/a+a=28

We move all terms to the left:

48/a+a-(28)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

a+48/a-28=0

We multiply all the terms by the denominator


a*a-28*a+48=0

We add all the numbers together, and all the variables

-28a+a*a+48=0

Wy multiply elements

a^2-28a+48=0

a = 1; b = -28; c = +48;
Δ = b2-4ac
Δ = -282-4·1·48
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{37}}{2*1}=\frac{28-4\sqrt{37}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{37}}{2*1}=\frac{28+4\sqrt{37}}{2}
$