48=x(x+5)

Solution for 48=x(x+5) equation:

48=x(x+5)

We move all terms to the left:

48-(x(x+5))=0


We calculate terms in parentheses: -(x(x+5)), so:

x(x+5)

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+48=0

We add all the numbers together, and all the variables

-1x^2-5x+48=0

a = -1; b = -5; c = +48;
Δ = b2-4ac
Δ = -52-4·(-1)·48
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*-1}=\frac{5-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*-1}=\frac{5+\sqrt{217}}{-2}
$