4900=x(48+x)

Solution for 4900=x(48+x) equation:

4900=x(48+x)

We move all terms to the left:

4900-(x(48+x))=0

We add all the numbers together, and all the variables

-(x(x+48))+4900=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+4900=0

We add all the numbers together, and all the variables

-1x^2-48x+4900=0

a = -1; b = -48; c = +4900;
Δ = b2-4ac
Δ = -482-4·(-1)·4900
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-148}{2*-1}=\frac{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+148}{2*-1}=\frac{196}{-2}
=-98
$