5x-2x/x=15

Solution for 5x-2x/x=15 equation:

5x-2x/x=15

We move all terms to the left:

5x-2x/x-(15)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-2x-15*x=0

We add all the numbers together, and all the variables

-17x+5x*x=0

Wy multiply elements

5x^2-17x=0

a = 5; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·5·0
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*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*5}=\frac{34}{10}
=3+2/5
$