410=x(x+4)

Solution for 410=x(x+4) equation:

410=x(x+4)

We move all terms to the left:

410-(x(x+4))=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+410=0

We add all the numbers together, and all the variables

-1x^2-4x+410=0

a = -1; b = -4; c = +410;
Δ = b2-4ac
Δ = -42-4·(-1)·410
Δ = 1656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{46}}{2*-1}=\frac{4-6\sqrt{46}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{46}}{2*-1}=\frac{4+6\sqrt{46}}{-2}
$