x=9(10x+10)(4x+20)

Solution for x=9(10x+10)(4x+20) equation:

x=9(10x+10)(4x+20)

We move all terms to the left:

x-(9(10x+10)(4x+20))=0

We multiply parentheses ..

-(9(+40x^2+200x+40x+200))+x=0


We calculate terms in parentheses: -(9(+40x^2+200x+40x+200)), so:

9(+40x^2+200x+40x+200)

We multiply parentheses

360x^2+1800x+360x+1800

We add all the numbers together, and all the variables

360x^2+2160x+1800

Back to the equation:

-(360x^2+2160x+1800)


We add all the numbers together, and all the variables

x-(360x^2+2160x+1800)=0

We get rid of parentheses

-360x^2+x-2160x-1800=0

We add all the numbers together, and all the variables

-360x^2-2159x-1800=0

a = -360; b = -2159; c = -1800;
Δ = b2-4ac
Δ = -21592-4·(-360)·(-1800)
Δ = 2069281
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{-(-2159)-\sqrt{2069281}}{2*-360}=\frac{2159-\sqrt{2069281}}{-720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2159)+\sqrt{2069281}}{2*-360}=\frac{2159+\sqrt{2069281}}{-720}
$