16x-10/x=27

Solution for 16x-10/x=27 equation:

16x-10/x=27

We move all terms to the left:

16x-10/x-(27)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


16x*x-27*x-10=0

We add all the numbers together, and all the variables

-27x+16x*x-10=0

Wy multiply elements

16x^2-27x-10=0

a = 16; b = -27; c = -10;
Δ = b2-4ac
Δ = -272-4·16·(-10)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-37}{2*16}=\frac{-10}{32}
=-5/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+37}{2*16}=\frac{64}{32}
=2
$