16(4-3x)=96(-1/2x+1)

Solution for 16(4-3x)=96(-1/2x+1) equation:

16(4-3x)=96(-1/2x+1)

We move all terms to the left:

16(4-3x)-(96(-1/2x+1))=0


Domain of the equation: 2x+1))!=0

x∈R


We add all the numbers together, and all the variables

16(-3x+4)-(96(-1/2x+1))=0

We multiply parentheses

-48x-(96(-1/2x+1))+64=0

We multiply all the terms by the denominator


-48x*2x+64*2x-1+1))-(96(+1))=0

We add all the numbers together, and all the variables

-48x*2x+64*2x-1+1))-(961)=0

We add all the numbers together, and all the variables

-48x*2x+64*2x=0

Wy multiply elements

-96x^2+128x=0

a = -96; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-96)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-96}=\frac{-256}{-192}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-96}=\frac{0}{-192}
=0
$