3/4x=420x

Solution for 3/4x=420x equation:

3/4x=420x

We move all terms to the left:

3/4x-(420x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-420x+3/4x=0

We multiply all the terms by the denominator


-420x*4x+3=0

Wy multiply elements

-1680x^2+3=0

a = -1680; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-1680)·3
Δ = 20160
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:

$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{35}}{2*-1680}=\frac{0-24\sqrt{35}}{-3360}
=-\frac{24\sqrt{35}}{-3360}
=-\frac{\sqrt{35}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{35}}{2*-1680}=\frac{0+24\sqrt{35}}{-3360}
=\frac{24\sqrt{35}}{-3360}
=\frac{\sqrt{35}}{-140}
$