1/3x=7x-48

Solution for 1/3x=7x-48 equation:

1/3x=7x-48

We move all terms to the left:

1/3x-(7x-48)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-7x+48=0

We multiply all the terms by the denominator


-7x*3x+48*3x+1=0

Wy multiply elements

-21x^2+144x+1=0

a = -21; b = 144; c = +1;
Δ = b2-4ac
Δ = 1442-4·(-21)·1
Δ = 20820
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:

$\sqrt{\Delta}=\sqrt{20820}=\sqrt{4*5205}=\sqrt{4}*\sqrt{5205}=2\sqrt{5205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{5205}}{2*-21}=\frac{-144-2\sqrt{5205}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{5205}}{2*-21}=\frac{-144+2\sqrt{5205}}{-42}
$