8272=x(x+48)

Solution for 8272=x(x+48) equation:

8272=x(x+48)

We move all terms to the left:

8272-(x(x+48))=0


We calculate terms in parentheses: -(x(x+48)), so:

x(x+48)

We multiply parentheses

x^2+48x

Back to the equation:

-(x^2+48x)


We get rid of parentheses

-x^2-48x+8272=0

We add all the numbers together, and all the variables

-1x^2-48x+8272=0

a = -1; b = -48; c = +8272;
Δ = b2-4ac
Δ = -482-4·(-1)·8272
Δ = 35392
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:

$\sqrt{\Delta}=\sqrt{35392}=\sqrt{64*553}=\sqrt{64}*\sqrt{553}=8\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{553}}{2*-1}=\frac{48-8\sqrt{553}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{553}}{2*-1}=\frac{48+8\sqrt{553}}{-2}
$