x^2/x=5x-17

Solution for x^2/x=5x-17 equation:

x^2/x=5x-17

We move all terms to the left:

x^2/x-(5x-17)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

x^2-5x^2+17x=0

We add all the numbers together, and all the variables

-4x^2+17x=0

a = -4; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-4)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-4}=\frac{-34}{-8}
=4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-4}=\frac{0}{-8}
=0
$