16-3x=10/x

Solution for 16-3x=10/x equation:

16-3x=10/x

We move all terms to the left:

16-3x-(10/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

-3x-(+10/x)+16=0

We get rid of parentheses

-3x-10/x+16=0

We multiply all the terms by the denominator


-3x*x+16*x-10=0

We add all the numbers together, and all the variables

16x-3x*x-10=0

Wy multiply elements

-3x^2+16x-10=0

a = -3; b = 16; c = -10;
Δ = b2-4ac
Δ = 162-4·(-3)·(-10)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{34}}{2*-3}=\frac{-16-2\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{34}}{2*-3}=\frac{-16+2\sqrt{34}}{-6}
$