18-x=1/3(15x)+6

Solution for 18-x=1/3(15x)+6 equation:

18-x=1/3(15x)+6

We move all terms to the left:

18-x-(1/3(15x)+6)=0


Domain of the equation: 315x+6)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/315x+6)+18=0

We get rid of parentheses

-1x-1/315x-6+18=0

We multiply all the terms by the denominator


-1x*315x-6*315x+18*315x-1=0

Wy multiply elements

-315x^2-1890x+5670x-1=0

We add all the numbers together, and all the variables

-315x^2+3780x-1=0

a = -315; b = 3780; c = -1;
Δ = b2-4ac
Δ = 37802-4·(-315)·(-1)
Δ = 14287140
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:

$\sqrt{\Delta}=\sqrt{14287140}=\sqrt{36*396865}=\sqrt{36}*\sqrt{396865}=6\sqrt{396865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3780)-6\sqrt{396865}}{2*-315}=\frac{-3780-6\sqrt{396865}}{-630}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3780)+6\sqrt{396865}}{2*-315}=\frac{-3780+6\sqrt{396865}}{-630}
$