3(1.5x-4)=3/2x-1.2

Solution for 3(1.5x-4)=3/2x-1.2 equation:

3(1.5x-4)=3/2x-1.2

We move all terms to the left:

3(1.5x-4)-(3/2x-1.2)=0


Domain of the equation: 2x-1.2)!=0

x∈R


We multiply parentheses

3x-(3/2x-1.2)-12=0

We get rid of parentheses

3x-3/2x+1.2-12=0

We multiply all the terms by the denominator


3x*2x+(1.2)*2x-12*2x-3=0

We multiply parentheses

3x*2x+2.4x-12*2x-3=0

Wy multiply elements

6x^2+2.4x-24x-3=0

We add all the numbers together, and all the variables

6x^2-21.6x-3=0

a = 6; b = -21.6; c = -3;
Δ = b2-4ac
Δ = -21.62-4·6·(-3)
Δ = 538.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21.6)-\sqrt{538.56}}{2*6}=\frac{21.6-\sqrt{538.56}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.6)+\sqrt{538.56}}{2*6}=\frac{21.6+\sqrt{538.56}}{12}
$