x=1/3x-48

Solution for x=1/3x-48 equation:

x=1/3x-48

We move all terms to the left:

x-(1/3x-48)=0


Domain of the equation: 3x-48)!=0

x∈R


We get rid of parentheses

x-1/3x+48=0

We multiply all the terms by the denominator


x*3x+48*3x-1=0

Wy multiply elements

3x^2+144x-1=0

a = 3; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·3·(-1)
Δ = 20748
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:

$\sqrt{\Delta}=\sqrt{20748}=\sqrt{4*5187}=\sqrt{4}*\sqrt{5187}=2\sqrt{5187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{5187}}{2*3}=\frac{-144-2\sqrt{5187}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{5187}}{2*3}=\frac{-144+2\sqrt{5187}}{6}
$