(5)/(2)x+(1)/(4)=(3)/(4)x+2

Solution for (5)/(2)x+(1)/(4)=(3)/(4)x+2 equation:

(5)/(2)x+(1)/(4)=(3)/(4)x+2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

5/2x-3/4x-2+1/4=0

We calculate fractions


320x/128x^2+(-6x)/128x^2+2x/128x^2-2=0

We multiply all the terms by the denominator


320x+(-6x)+2x-2*128x^2=0

We add all the numbers together, and all the variables

322x+(-6x)-2*128x^2=0

Wy multiply elements

-256x^2+322x+(-6x)=0

We get rid of parentheses

-256x^2+322x-6x=0

We add all the numbers together, and all the variables

-256x^2+316x=0

a = -256; b = 316; c = 0;
Δ = b2-4ac
Δ = 3162-4·(-256)·0
Δ = 99856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99856}=316$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(316)-316}{2*-256}=\frac{-632}{-512}
=1+15/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(316)+316}{2*-256}=\frac{0}{-512}
=0
$