x+6=1/3x+1.5

Solution for x+6=1/3x+1.5 equation:

x+6=1/3x+1.5

We move all terms to the left:

x+6-(1/3x+1.5)=0


Domain of the equation: 3x+1.5)!=0

x∈R


We get rid of parentheses

x-1/3x-1.5+6=0

We multiply all the terms by the denominator


x*3x-(1.5)*3x+6*3x-1=0

We multiply parentheses

x*3x-4.5x+6*3x-1=0

Wy multiply elements

3x^2-4.5x+18x-1=0

We add all the numbers together, and all the variables

3x^2+13.5x-1=0

a = 3; b = 13.5; c = -1;
Δ = b2-4ac
Δ = 13.52-4·3·(-1)
Δ = 194.25
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{-(13.5)-\sqrt{194.25}}{2*3}=\frac{-13.5-\sqrt{194.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13.5)+\sqrt{194.25}}{2*3}=\frac{-13.5+\sqrt{194.25}}{6}
$