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

Solution for 0,5x+2-1/4x=3 equation:

0.5x+2-1/4x=3

We move all terms to the left:

0.5x+2-1/4x-(3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

0.5x-1/4x-1=0

We multiply all the terms by the denominator


(0.5x)*4x-1*4x-1=0

We add all the numbers together, and all the variables

(+0.5x)*4x-1*4x-1=0

We multiply parentheses

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

Wy multiply elements

0x^2-4x-1=0

We add all the numbers together, and all the variables

x^2-4x-1=0

a = 1; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·1·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{5}}{2*1}=\frac{4-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{5}}{2*1}=\frac{4+2\sqrt{5}}{2}
$