x+x*x+x*x*5=x*x*6

Solution for x+x*x+x*x*5=x*x*6 equation:

x+x*x+x*x*5=x*x*6

We move all terms to the left:

x+x*x+x*x*5-(x*x*6)=0

We add all the numbers together, and all the variables

x+x*x+x*x*5-(+x*x*6)=0

Wy multiply elements

x^2+5x^2*5+x-(+x*x*6)=0

We get rid of parentheses

x^2+5x^2*5+x-x*x*6=0

Wy multiply elements

x^2+25x^2-6x^2*6+x=0

We add all the numbers together, and all the variables

26x^2-6x^2*6+x=0

Wy multiply elements

26x^2-36x^2+x=0

We add all the numbers together, and all the variables

-10x^2+x=0

a = -10; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-10)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-10}=\frac{-2}{-20}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-10}=\frac{0}{-20}
=0
$