5x-42=1/3x

Solution for 5x-42=1/3x equation:

5x-42=1/3x

We move all terms to the left:

5x-42-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/3x)-42=0

We get rid of parentheses

5x-1/3x-42=0

We multiply all the terms by the denominator


5x*3x-42*3x-1=0

Wy multiply elements

15x^2-126x-1=0

a = 15; b = -126; c = -1;
Δ = b2-4ac
Δ = -1262-4·15·(-1)
Δ = 15936
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:

$\sqrt{\Delta}=\sqrt{15936}=\sqrt{64*249}=\sqrt{64}*\sqrt{249}=8\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-8\sqrt{249}}{2*15}=\frac{126-8\sqrt{249}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+8\sqrt{249}}{2*15}=\frac{126+8\sqrt{249}}{30}
$