6/5x=15x

Solution for 6/5x=15x equation:

6/5x=15x

We move all terms to the left:

6/5x-(15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-15x+6/5x=0

We multiply all the terms by the denominator


-15x*5x+6=0

Wy multiply elements

-75x^2+6=0

a = -75; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-75)·6
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*-75}=\frac{0-30\sqrt{2}}{-150}
=-\frac{30\sqrt{2}}{-150}
=-\frac{\sqrt{2}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*-75}=\frac{0+30\sqrt{2}}{-150}
=\frac{30\sqrt{2}}{-150}
=\frac{\sqrt{2}}{-5}
$