413=x*1.42x

Solution for 413=x*1.42x equation:

413=x*1.42x

We move all terms to the left:

413-(x*1.42x)=0

We add all the numbers together, and all the variables

-(+x*1.42x)+413=0

We get rid of parentheses

-x*1.42x+413=0

Wy multiply elements

-1x^2+413=0

a = -1; b = 0; c = +413;
Δ = b2-4ac
Δ = 02-4·(-1)·413
Δ = 1652
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:

$\sqrt{\Delta}=\sqrt{1652}=\sqrt{4*413}=\sqrt{4}*\sqrt{413}=2\sqrt{413}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{413}}{2*-1}=\frac{0-2\sqrt{413}}{-2}
=-\frac{2\sqrt{413}}{-2}
=-\frac{\sqrt{413}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{413}}{2*-1}=\frac{0+2\sqrt{413}}{-2}
=\frac{2\sqrt{413}}{-2}
=\frac{\sqrt{413}}{-1}
$