3/13x=18x

Solution for 3/13x=18x equation:

3/13x=18x

We move all terms to the left:

3/13x-(18x)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

-18x+3/13x=0

We multiply all the terms by the denominator


-18x*13x+3=0

Wy multiply elements

-234x^2+3=0

a = -234; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-234)·3
Δ = 2808
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:

$\sqrt{\Delta}=\sqrt{2808}=\sqrt{36*78}=\sqrt{36}*\sqrt{78}=6\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{78}}{2*-234}=\frac{0-6\sqrt{78}}{-468}
=-\frac{6\sqrt{78}}{-468}
=-\frac{\sqrt{78}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{78}}{2*-234}=\frac{0+6\sqrt{78}}{-468}
=\frac{6\sqrt{78}}{-468}
=\frac{\sqrt{78}}{-78}
$