0.5x+3/4x=5/4x-x

Solution for 0.5x+3/4x=5/4x-x equation:

0.5x+3/4x=5/4x-x

We move all terms to the left:

0.5x+3/4x-(5/4x-x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x-x)!=0

x∈R


We add all the numbers together, and all the variables

0.5x+3/4x-(-1x+5/4x)=0

We get rid of parentheses

0.5x+3/4x+1x-5/4x=0

We multiply all the terms by the denominator


(0.5x)*4x+1x*4x+3-5=0

We add all the numbers together, and all the variables

(+0.5x)*4x+1x*4x+3-5=0

We add all the numbers together, and all the variables

(+0.5x)*4x+1x*4x-2=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

5x^2-2=0

a = 5; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·5·(-2)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*5}=\frac{0-2\sqrt{10}}{10}
=-\frac{2\sqrt{10}}{10}
=-\frac{\sqrt{10}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*5}=\frac{0+2\sqrt{10}}{10}
=\frac{2\sqrt{10}}{10}
=\frac{\sqrt{10}}{5}
$