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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-4+1/4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*4-15=0

Wy multiply elements

4x^2-15=0

a = 4; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·4·(-15)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*4}=\frac{0-4\sqrt{15}}{8}
=-\frac{4\sqrt{15}}{8}
=-\frac{\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*4}=\frac{0+4\sqrt{15}}{8}
=\frac{4\sqrt{15}}{8}
=\frac{\sqrt{15}}{2}
$