48=x(x+13)

Solution for 48=x(x+13) equation:

48=x(x+13)

We move all terms to the left:

48-(x(x+13))=0


We calculate terms in parentheses: -(x(x+13)), so:

x(x+13)

We multiply parentheses

x^2+13x

Back to the equation:

-(x^2+13x)


We get rid of parentheses

-x^2-13x+48=0

We add all the numbers together, and all the variables

-1x^2-13x+48=0

a = -1; b = -13; c = +48;
Δ = b2-4ac
Δ = -132-4·(-1)·48
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*-1}=\frac{32}{-2}
=-16
$