64/x+17=2x+9

Solution for 64/x+17=2x+9 equation:

64/x+17=2x+9

We move all terms to the left:

64/x+17-(2x+9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

64/x-2x-9+17=0

We multiply all the terms by the denominator


-2x*x-9*x+17*x+64=0

We add all the numbers together, and all the variables

8x-2x*x+64=0

Wy multiply elements

-2x^2+8x+64=0

a = -2; b = 8; c = +64;
Δ = b2-4ac
Δ = 82-4·(-2)·64
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*-2}=\frac{16}{-4}
=-4
$