x*(48+x)=3897

Solution for x*(48+x)=3897 equation:

x(48+x)=3897

We move all terms to the left:

x(48+x)-(3897)=0

We add all the numbers together, and all the variables

x(x+48)-3897=0

We multiply parentheses

x^2+48x-3897=0

a = 1; b = 48; c = -3897;
Δ = b2-4ac
Δ = 482-4·1·(-3897)
Δ = 17892
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:

$\sqrt{\Delta}=\sqrt{17892}=\sqrt{36*497}=\sqrt{36}*\sqrt{497}=6\sqrt{497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{497}}{2*1}=\frac{-48-6\sqrt{497}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{497}}{2*1}=\frac{-48+6\sqrt{497}}{2}
$