x/2x+4-x=4X-5

Solution for x/2x+4-x=4X-5 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1x*2x+x-4x*2x+5*2x+4*2x=0

We add all the numbers together, and all the variables

x-1x*2x-4x*2x+5*2x+4*2x=0

Wy multiply elements

-2x^2-8x^2+x+10x+8x=0

We add all the numbers together, and all the variables

-10x^2+19x=0

a = -10; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-10)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-10}=\frac{-38}{-20}
=1+9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-10}=\frac{0}{-20}
=0
$