1.5*x+4=2/3*x+19

Solution for 1.5*x+4=2/3*x+19 equation:

1.5x+4=2/3x+19

We move all terms to the left:

1.5x+4-(2/3x+19)=0


Domain of the equation: 3x+19)!=0

x∈R


We get rid of parentheses

1.5x-2/3x-19+4=0

We multiply all the terms by the denominator


(1.5x)*3x-19*3x+4*3x-2=0

We add all the numbers together, and all the variables

(+1.5x)*3x-19*3x+4*3x-2=0

We multiply parentheses

3x^2-19*3x+4*3x-2=0

Wy multiply elements

3x^2-57x+12x-2=0

We add all the numbers together, and all the variables

3x^2-45x-2=0

a = 3; b = -45; c = -2;
Δ = b2-4ac
Δ = -452-4·3·(-2)
Δ = 2049
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{-(-45)-\sqrt{2049}}{2*3}=\frac{45-\sqrt{2049}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*3}=\frac{45+\sqrt{2049}}{6}
$