x-79/x=16

Solution for x-79/x=16 equation:

x-79/x=16

We move all terms to the left:

x-79/x-(16)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-16*x-79=0

We add all the numbers together, and all the variables

-16x+x*x-79=0

Wy multiply elements

x^2-16x-79=0

a = 1; b = -16; c = -79;
Δ = b2-4ac
Δ = -162-4·1·(-79)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{143}}{2*1}=\frac{16-2\sqrt{143}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{143}}{2*1}=\frac{16+2\sqrt{143}}{2}
$