x-2*1/2x+4=-8

Solution for x-2*1/2x+4=-8 equation:

x-2*1/2x+4=-8

We move all terms to the left:

x-2*1/2x+4-(-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x-2*1/2x+12=0

We multiply all the terms by the denominator


x*2x+12*2x-2*1=0

We add all the numbers together, and all the variables

x*2x+12*2x-2=0

Wy multiply elements

2x^2+24x-2=0

a = 2; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·2·(-2)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{37}}{2*2}=\frac{-24-4\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{37}}{2*2}=\frac{-24+4\sqrt{37}}{4}
$