41/2x-3/4=3-1/4x

Solution for 41/2x-3/4=3-1/4x equation:

41/2x-3/4=3-1/4x

We move all terms to the left:

41/2x-3/4-(3-1/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

41/2x-(-1/4x+3)-3/4=0

We get rid of parentheses

41/2x+1/4x-3-3/4=0

We calculate fractions


2624x/128x^2+2x/128x^2+(-6x)/128x^2-3=0

We multiply all the terms by the denominator


2624x+2x+(-6x)-3*128x^2=0

We add all the numbers together, and all the variables

2626x+(-6x)-3*128x^2=0

Wy multiply elements

-384x^2+2626x+(-6x)=0

We get rid of parentheses

-384x^2+2626x-6x=0

We add all the numbers together, and all the variables

-384x^2+2620x=0

a = -384; b = 2620; c = 0;
Δ = b2-4ac
Δ = 26202-4·(-384)·0
Δ = 6864400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6864400}=2620$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2620)-2620}{2*-384}=\frac{-5240}{-768}
=6+79/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2620)+2620}{2*-384}=\frac{0}{-768}
=0
$