480=x(x+14)

Solution for 480=x(x+14) equation:

480=x(x+14)

We move all terms to the left:

480-(x(x+14))=0


We calculate terms in parentheses: -(x(x+14)), so:

x(x+14)

We multiply parentheses

x^2+14x

Back to the equation:

-(x^2+14x)


We get rid of parentheses

-x^2-14x+480=0

We add all the numbers together, and all the variables

-1x^2-14x+480=0

a = -1; b = -14; c = +480;
Δ = b2-4ac
Δ = -142-4·(-1)·480
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-46}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+46}{2*-1}=\frac{60}{-2}
=-30
$