5/2x-6/4x=-1

Solution for 5/2x-6/4x=-1 equation:

5/2x-6/4x=-1

We move all terms to the left:

5/2x-6/4x-(-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-6/4x+1=0

We calculate fractions


20x/8x^2+(-12x)/8x^2+1=0

We multiply all the terms by the denominator


20x+(-12x)+1*8x^2=0

Wy multiply elements

8x^2+20x+(-12x)=0

We get rid of parentheses

8x^2+20x-12x=0

We add all the numbers together, and all the variables

8x^2+8x=0

a = 8; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·8·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*8}=\frac{0}{16}
=0
$