2/3x-1.5=6x-12

Solution for 2/3x-1.5=6x-12 equation:

2/3x-1.5=6x-12

We move all terms to the left:

2/3x-1.5-(6x-12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-6x+12-1.5=0

We multiply all the terms by the denominator


-6x*3x+12*3x-(1.5)*3x+2=0

We multiply parentheses

-6x*3x+12*3x-4.5x+2=0

Wy multiply elements

-18x^2+36x-4.5x+2=0

We add all the numbers together, and all the variables

-18x^2+31.5x+2=0

a = -18; b = 31.5; c = +2;
Δ = b2-4ac
Δ = 31.52-4·(-18)·2
Δ = 1136.25
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{-(31.5)-\sqrt{1136.25}}{2*-18}=\frac{-31.5-\sqrt{1136.25}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.5)+\sqrt{1136.25}}{2*-18}=\frac{-31.5+\sqrt{1136.25}}{-36}
$