X+96/x=40

Solution for X+96/x=40 equation:

X+96/X=40

We move all terms to the left:

X+96/X-(40)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-40*X+96=0

We add all the numbers together, and all the variables

-40X+X*X+96=0

Wy multiply elements

X^2-40X+96=0

a = 1; b = -40; c = +96;
Δ = b2-4ac
Δ = -402-4·1·96
Δ = 1216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{19}}{2*1}=\frac{40-8\sqrt{19}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{19}}{2*1}=\frac{40+8\sqrt{19}}{2}
$