x=x*3x-5

Solution for x=x*3x-5 equation:

x=x*3x-5

We move all terms to the left:

x-(x*3x-5)=0

We get rid of parentheses

x-x*3x+5=0

Wy multiply elements

-3x^2+x+5=0

a = -3; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-3)·5
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{61}}{2*-3}=\frac{-1-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*-3}=\frac{-1+\sqrt{61}}{-6}
$