1/2x+4=2x-0.5

Solution for 1/2x+4=2x-0.5 equation:

1/2x+4=2x-0.5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x+0.5+4=0

We multiply all the terms by the denominator


-2x*2x+(0.5)*2x+4*2x+1=0

We multiply parentheses

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

Wy multiply elements

-4x^2+x+8x+1=0

We add all the numbers together, and all the variables

-4x^2+9x+1=0

a = -4; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-4)·1
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{97}}{2*-4}=\frac{-9-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{97}}{2*-4}=\frac{-9+\sqrt{97}}{-8}
$