50+8x=100/x

Solution for 50+8x=100/x equation:

50+8x=100/x

We move all terms to the left:

50+8x-(100/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+100/x)+50=0

We get rid of parentheses

8x-100/x+50=0

We multiply all the terms by the denominator


8x*x+50*x-100=0

We add all the numbers together, and all the variables

50x+8x*x-100=0

Wy multiply elements

8x^2+50x-100=0

a = 8; b = 50; c = -100;
Δ = b2-4ac
Δ = 502-4·8·(-100)
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{57}}{2*8}=\frac{-50-10\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{57}}{2*8}=\frac{-50+10\sqrt{57}}{16}
$