16x-24=8(1/2x-12)

Solution for 16x-24=8(1/2x-12) equation:

16x-24=8(1/2x-12)

We move all terms to the left:

16x-24-(8(1/2x-12))=0


Domain of the equation: 2x-12))!=0

x∈R


We multiply all the terms by the denominator


16x*2x-24*2x-12))-(8(1-12))=0

We add all the numbers together, and all the variables

16x*2x-24*2x-12))-(8(-11))=0

We add all the numbers together, and all the variables

16x*2x-24*2x=0

Wy multiply elements

32x^2-48x=0

a = 32; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·32·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*32}=\frac{0}{64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*32}=\frac{96}{64}
=1+1/2
$