60-1/3x=3x

Solution for 60-1/3x=3x equation:

60-1/3x=3x

We move all terms to the left:

60-1/3x-(3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x-1/3x+60=0

We multiply all the terms by the denominator


-3x*3x+60*3x-1=0

Wy multiply elements

-9x^2+180x-1=0

a = -9; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·(-9)·(-1)
Δ = 32364
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:

$\sqrt{\Delta}=\sqrt{32364}=\sqrt{36*899}=\sqrt{36}*\sqrt{899}=6\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{899}}{2*-9}=\frac{-180-6\sqrt{899}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{899}}{2*-9}=\frac{-180+6\sqrt{899}}{-18}
$