5x/2x-3=4x

Solution for 5x/2x-3=4x equation:

5x/2x-3=4x

We move all terms to the left:

5x/2x-3-(4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+5x/2x-3=0

We multiply all the terms by the denominator


-4x*2x+5x-3*2x=0

We add all the numbers together, and all the variables

5x-4x*2x-3*2x=0

Wy multiply elements

-8x^2+5x-6x=0

We add all the numbers together, and all the variables

-8x^2-1x=0

a = -8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-8)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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