1.5x-12=2/3x-1.4

Solution for 1.5x-12=2/3x-1.4 equation:

1.5x-12=2/3x-1.4

We move all terms to the left:

1.5x-12-(2/3x-1.4)=0


Domain of the equation: 3x-1.4)!=0

x∈R


We get rid of parentheses

1.5x-2/3x+1.4-12=0

We multiply all the terms by the denominator


(1.5x)*3x+(1.4)*3x-12*3x-2=0

We add all the numbers together, and all the variables

(+1.5x)*3x+(1.4)*3x-12*3x-2=0

We multiply parentheses

3x^2+4.2x-12*3x-2=0

Wy multiply elements

3x^2+4.2x-36x-2=0

We add all the numbers together, and all the variables

3x^2-31.8x-2=0

a = 3; b = -31.8; c = -2;
Δ = b2-4ac
Δ = -31.82-4·3·(-2)
Δ = 1035.24
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{-(-31.8)-\sqrt{1035.24}}{2*3}=\frac{31.8-\sqrt{1035.24}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31.8)+\sqrt{1035.24}}{2*3}=\frac{31.8+\sqrt{1035.24}}{6}
$