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

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

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

We move all terms to the left:

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


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

r∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

r^2-21.6r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21.6)-\sqrt{478.56}}{2*1}=\frac{21.6-\sqrt{478.56}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.6)+\sqrt{478.56}}{2*1}=\frac{21.6+\sqrt{478.56}}{2}
$