1000=(X-20)(x-20)(10)

Solution for 1000=(X-20)(x-20)(10) equation:

1000=(X-20)(X-20)(10)

We move all terms to the left:

1000-((X-20)(X-20)(10))=0

We multiply parentheses ..

-((+X^2-20X-20X+400)10)+1000=0


We calculate terms in parentheses: -((+X^2-20X-20X+400)10), so:

(+X^2-20X-20X+400)10

We multiply parentheses

10X^2-200X-200X+4000

We add all the numbers together, and all the variables

10X^2-400X+4000

Back to the equation:

-(10X^2-400X+4000)


We get rid of parentheses

-10X^2+400X-4000+1000=0

We add all the numbers together, and all the variables

-10X^2+400X-3000=0

a = -10; b = 400; c = -3000;
Δ = b2-4ac
Δ = 4002-4·(-10)·(-3000)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-200}{2*-10}=\frac{-600}{-20}
=+30
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+200}{2*-10}=\frac{-200}{-20}
=+10
$