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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

x^2-x-3-1/4=0

We multiply all the terms by the denominator


x^2*4-x*4-1-3*4=0

We add all the numbers together, and all the variables

x^2*4-x*4-13=0

Wy multiply elements

4x^2-4x-13=0

a = 4; b = -4; c = -13;
Δ = b2-4ac
Δ = -42-4·4·(-13)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{14}}{2*4}=\frac{4-4\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{14}}{2*4}=\frac{4+4\sqrt{14}}{8}
$