5/x+17=2x-1

Solution for 5/x+17=2x-1 equation:

5/x+17=2x-1

We move all terms to the left:

5/x+17-(2x-1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-2x+1+17=0

We multiply all the terms by the denominator


-2x*x+1*x+17*x+5=0

We add all the numbers together, and all the variables

18x-2x*x+5=0

Wy multiply elements

-2x^2+18x+5=0

a = -2; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-2)·5
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{91}}{2*-2}=\frac{-18-2\sqrt{91}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{91}}{2*-2}=\frac{-18+2\sqrt{91}}{-4}
$