x(45-5x)=x

Solution for x(45-5x)=x equation:

x(45-5x)=x

We move all terms to the left:

x(45-5x)-(x)=0

We add all the numbers together, and all the variables

x(-5x+45)-x=0

We add all the numbers together, and all the variables

-1x+x(-5x+45)=0

We multiply parentheses

-5x^2-1x+45x=0

We add all the numbers together, and all the variables

-5x^2+44x=0

a = -5; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-5)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-5}=\frac{-88}{-10}
=8+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-5}=\frac{0}{-10}
=0
$