x*(4+x)=3897

Solution for x*(4+x)=3897 equation:

x(4+x)=3897

We move all terms to the left:

x(4+x)-(3897)=0

We add all the numbers together, and all the variables

x(x+4)-3897=0

We multiply parentheses

x^2+4x-3897=0

a = 1; b = 4; c = -3897;
Δ = b2-4ac
Δ = 42-4·1·(-3897)
Δ = 15604
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:

$\sqrt{\Delta}=\sqrt{15604}=\sqrt{4*3901}=\sqrt{4}*\sqrt{3901}=2\sqrt{3901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{3901}}{2*1}=\frac{-4-2\sqrt{3901}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{3901}}{2*1}=\frac{-4+2\sqrt{3901}}{2}
$