(1/2)x+2=1/4+6

Solution for (1/2)x+2=1/4+6 equation:

(1/2)x+2=1/4+6

We move all terms to the left:

(1/2)x+2-(1/4+6)=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+2-(1/4+6)=0

We multiply parentheses

x^2+2-(1/4+6)=0

We get rid of parentheses

x^2+2-6-1/4=0

We multiply all the terms by the denominator


x^2*4-1+2*4-6*4=0

We add all the numbers together, and all the variables

x^2*4-17=0

Wy multiply elements

4x^2-17=0

a = 4; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·4·(-17)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{17}}{2*4}=\frac{0-4\sqrt{17}}{8}
=-\frac{4\sqrt{17}}{8}
=-\frac{\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{17}}{2*4}=\frac{0+4\sqrt{17}}{8}
=\frac{4\sqrt{17}}{8}
=\frac{\sqrt{17}}{2}
$