3(0.5x-4)=(3)/(2)x-1.2

Solution for 3(0.5x-4)=(3)/(2)x-1.2 equation:

3(0.5x-4)=(3)/(2)x-1.2

We move all terms to the left:

3(0.5x-4)-((3)/(2)x-1.2)=0


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

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2-21.6x-3=0

a = 1; b = -21.6; c = -3;
Δ = b2-4ac
Δ = -21.62-4·1·(-3)
Δ = 478.56
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{478.56}}{2*1}=\frac{21.6-\sqrt{478.56}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.6)+\sqrt{478.56}}{2*1}=\frac{21.6+\sqrt{478.56}}{2}
$