1/2x-2+1/2x-2=3x-24

Solution for 1/2x-2+1/2x-2=3x-24 equation:

1/2x-2+1/2x-2=3x-24

We move all terms to the left:

1/2x-2+1/2x-2-(3x-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

1/2x+1/2x-(3x-24)-4=0

We get rid of parentheses

1/2x+1/2x-3x+24-4=0

We multiply all the terms by the denominator


-3x*2x+24*2x-4*2x+1+1=0

We add all the numbers together, and all the variables

-3x*2x+24*2x-4*2x+2=0

Wy multiply elements

-6x^2+48x-8x+2=0

We add all the numbers together, and all the variables

-6x^2+40x+2=0

a = -6; b = 40; c = +2;
Δ = b2-4ac
Δ = 402-4·(-6)·2
Δ = 1648
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:

$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{103}}{2*-6}=\frac{-40-4\sqrt{103}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{103}}{2*-6}=\frac{-40+4\sqrt{103}}{-12}
$