1/3x=3x-56

Solution for 1/3x=3x-56 equation:

1/3x=3x-56

We move all terms to the left:

1/3x-(3x-56)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-3x+56=0

We multiply all the terms by the denominator


-3x*3x+56*3x+1=0

Wy multiply elements

-9x^2+168x+1=0

a = -9; b = 168; c = +1;
Δ = b2-4ac
Δ = 1682-4·(-9)·1
Δ = 28260
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:

$\sqrt{\Delta}=\sqrt{28260}=\sqrt{36*785}=\sqrt{36}*\sqrt{785}=6\sqrt{785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-6\sqrt{785}}{2*-9}=\frac{-168-6\sqrt{785}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+6\sqrt{785}}{2*-9}=\frac{-168+6\sqrt{785}}{-18}
$