3x/4x=2x-5

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

3x/4x=2x-5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+3x+20x=0

We add all the numbers together, and all the variables

-8x^2+23x=0

a = -8; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-8)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-8}=\frac{-46}{-16}
=2+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-8}=\frac{0}{-16}
=0
$