450/3x=6+x

Solution for 450/3x=6+x equation:

450/3x=6+x

We move all terms to the left:

450/3x-(6+x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

450/3x-(x+6)=0

We get rid of parentheses

450/3x-x-6=0

We multiply all the terms by the denominator


-x*3x-6*3x+450=0

Wy multiply elements

-3x^2-18x+450=0

a = -3; b = -18; c = +450;
Δ = b2-4ac
Δ = -182-4·(-3)·450
Δ = 5724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5724}=\sqrt{36*159}=\sqrt{36}*\sqrt{159}=6\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{159}}{2*-3}=\frac{18-6\sqrt{159}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{159}}{2*-3}=\frac{18+6\sqrt{159}}{-6}
$