3(0.5x-4)=3/2x-12

Solution for 3(0.5x-4)=3/2x-12 equation:

3(0.5x-4)=3/2x-12

We move all terms to the left:

3(0.5x-4)-(3/2x-12)=0


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

x∈R


We multiply parentheses

0x-(3/2x-12)-12=0

We get rid of parentheses

0x-3/2x+12-12=0

We multiply all the terms by the denominator


0x*2x+12*2x-12*2x-3=0

Wy multiply elements

0x^2+24x-24x-3=0

We add all the numbers together, and all the variables

x^2-3=0

a = 1; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1·(-3)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*1}=\frac{0-2\sqrt{3}}{2}
=-\frac{2\sqrt{3}}{2}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*1}=\frac{0+2\sqrt{3}}{2}
=\frac{2\sqrt{3}}{2}
=\sqrt{3}
$