2(3/2x+-3)=-24(3/8x+-6)

Solution for 2(3/2x+-3)=-24(3/8x+-6) equation:

2(3/2x+-3)=-24(3/8x+-6)

We move all terms to the left:

2(3/2x+-3)-(-24(3/8x+-6))=0


Domain of the equation: 2x+-3)!=0

x∈R



Domain of the equation: 8x+-6))!=0

x∈R


We add all the numbers together, and all the variables

2(3/2x-3)-(-24(3/8x-6))=0

We multiply parentheses

6x-(-24(3/8x-6))-6=0

We multiply all the terms by the denominator


6x*8x-6*8x-6))-(-24(3-6))=0

We add all the numbers together, and all the variables

6x*8x-6*8x-6))-(-24(-3))=0

We add all the numbers together, and all the variables

6x*8x-6*8x=0

Wy multiply elements

48x^2-48x=0

a = 48; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·48·0
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*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*48}=\frac{96}{96}
=1
$