1/2x-x=-24

Solution for 1/2x-x=-24 equation:

1/2x-x=-24

We move all terms to the left:

1/2x-x-(-24)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x+24=0

We multiply all the terms by the denominator


-1x*2x+24*2x+1=0

Wy multiply elements

-2x^2+48x+1=0

a = -2; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-2)·1
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-34\sqrt{2}}{2*-2}=\frac{-48-34\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+34\sqrt{2}}{2*-2}=\frac{-48+34\sqrt{2}}{-4}
$