4x(5x+45)=x

Solution for 4x(5x+45)=x equation:

4x(5x+45)=x

We move all terms to the left:

4x(5x+45)-(x)=0

We add all the numbers together, and all the variables

-1x+4x(5x+45)=0

We multiply parentheses

20x^2-1x+180x=0

We add all the numbers together, and all the variables

20x^2+179x=0

a = 20; b = 179; c = 0;
Δ = b2-4ac
Δ = 1792-4·20·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(179)-179}{2*20}=\frac{-358}{40}
=-8+19/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(179)+179}{2*20}=\frac{0}{40}
=0
$