2+31/4x=12+51/2x

Solution for 2+31/4x=12+51/2x equation:

2+31/4x=12+51/2x

We move all terms to the left:

2+31/4x-(12+51/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

31/4x-(51/2x+12)+2=0

We get rid of parentheses

31/4x-51/2x-12+2=0

We calculate fractions


62x/8x^2+(-204x)/8x^2-12+2=0

We add all the numbers together, and all the variables

62x/8x^2+(-204x)/8x^2-10=0

We multiply all the terms by the denominator


62x+(-204x)-10*8x^2=0

Wy multiply elements

-80x^2+62x+(-204x)=0

We get rid of parentheses

-80x^2+62x-204x=0

We add all the numbers together, and all the variables

-80x^2-142x=0

a = -80; b = -142; c = 0;
Δ = b2-4ac
Δ = -1422-4·(-80)·0
Δ = 20164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20164}=142$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-142}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+142}{2*-80}=\frac{284}{-160}
=-1+31/40
$