x*(1+48x)=3897

Solution for x*(1+48x)=3897 equation:

x(1+48x)=3897

We move all terms to the left:

x(1+48x)-(3897)=0

We add all the numbers together, and all the variables

x(48x+1)-3897=0

We multiply parentheses

48x^2+x-3897=0

a = 48; b = 1; c = -3897;
Δ = b2-4ac
Δ = 12-4·48·(-3897)
Δ = 748225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{748225}=865$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-865}{2*48}=\frac{-866}{96}
=-9+1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+865}{2*48}=\frac{864}{96}
=9
$