x/5x-3/4=2x

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

x/5x-3/4=2x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


-2x+4x/20x+(-15x)/20x=0

We multiply all the terms by the denominator


-2x*20x+4x+(-15x)=0

We add all the numbers together, and all the variables

4x-2x*20x+(-15x)=0

Wy multiply elements

-40x^2+4x+(-15x)=0

We get rid of parentheses

-40x^2+4x-15x=0

We add all the numbers together, and all the variables

-40x^2-11x=0

a = -40; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-40)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-40}=\frac{22}{-80}
=-11/40
$