6/5x=90;x=1/15

Solution for 6/5x=90;x=1/15 equation:

6/5x=90x=1/15

We move all terms to the left:

6/5x-(90x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-90x+6/5x=0

We multiply all the terms by the denominator


-90x*5x+6=0

Wy multiply elements

-450x^2+6=0

a = -450; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-450)·6
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{3}}{2*-450}=\frac{0-60\sqrt{3}}{-900}
=-\frac{60\sqrt{3}}{-900}
=-\frac{\sqrt{3}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{3}}{2*-450}=\frac{0+60\sqrt{3}}{-900}
=\frac{60\sqrt{3}}{-900}
=\frac{\sqrt{3}}{-15}
$