x(105+x)=4

Solution for x(105+x)=4 equation:

x(105+x)=4

We move all terms to the left:

x(105+x)-(4)=0

We add all the numbers together, and all the variables

x(x+105)-4=0

We multiply parentheses

x^2+105x-4=0

a = 1; b = 105; c = -4;
Δ = b2-4ac
Δ = 1052-4·1·(-4)
Δ = 11041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-\sqrt{11041}}{2*1}=\frac{-105-\sqrt{11041}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11041}}{2*1}=\frac{-105+\sqrt{11041}}{2}
$