406.25=x(x+20)

Solution for 406.25=x(x+20) equation:

406.25=x(x+20)

We move all terms to the left:

406.25-(x(x+20))=0


We calculate terms in parentheses: -(x(x+20)), so:

x(x+20)

We multiply parentheses

x^2+20x

Back to the equation:

-(x^2+20x)


We get rid of parentheses

-x^2-20x+406.25=0

We add all the numbers together, and all the variables

-1x^2-20x+406.25=0

a = -1; b = -20; c = +406.25;
Δ = b2-4ac
Δ = -202-4·(-1)·406.25
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-45}{2*-1}=\frac{-25}{-2}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+45}{2*-1}=\frac{65}{-2}
=-32+1/2
$