1/3x=x-154

Solution for 1/3x=x-154 equation:

1/3x=x-154

We move all terms to the left:

1/3x-(x-154)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+154=0

We multiply all the terms by the denominator


-x*3x+154*3x+1=0

Wy multiply elements

-3x^2+462x+1=0

a = -3; b = 462; c = +1;
Δ = b2-4ac
Δ = 4622-4·(-3)·1
Δ = 213456
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:

$\sqrt{\Delta}=\sqrt{213456}=\sqrt{16*13341}=\sqrt{16}*\sqrt{13341}=4\sqrt{13341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-4\sqrt{13341}}{2*-3}=\frac{-462-4\sqrt{13341}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+4\sqrt{13341}}{2*-3}=\frac{-462+4\sqrt{13341}}{-6}
$