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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/32x^2+(-24x)/32x^2+(-20x)/32x^2+2=0

We multiply all the terms by the denominator


4x+(-24x)+(-20x)+2*32x^2=0

Wy multiply elements

64x^2+4x+(-24x)+(-20x)=0

We get rid of parentheses

64x^2+4x-24x-20x=0

We add all the numbers together, and all the variables

64x^2-40x=0

a = 64; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·64·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*64}=\frac{80}{128}
=5/8
$