5x/2x-1x=-5

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

5x/2x-1x=-5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2+5x+10x=0

We add all the numbers together, and all the variables

-2x^2+15x=0

a = -2; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-2)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-2}=\frac{0}{-4}
=0
$