15x+42=1/3x

Solution for 15x+42=1/3x equation:

15x+42=1/3x

We move all terms to the left:

15x+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

15x-(+1/3x)+42=0

We get rid of parentheses

15x-1/3x+42=0

We multiply all the terms by the denominator


15x*3x+42*3x-1=0

Wy multiply elements

45x^2+126x-1=0

a = 45; b = 126; c = -1;
Δ = b2-4ac
Δ = 1262-4·45·(-1)
Δ = 16056
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:

$\sqrt{\Delta}=\sqrt{16056}=\sqrt{36*446}=\sqrt{36}*\sqrt{446}=6\sqrt{446}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{446}}{2*45}=\frac{-126-6\sqrt{446}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{446}}{2*45}=\frac{-126+6\sqrt{446}}{90}
$