x*(x+1)-47x=360

Solution for x*(x+1)-47x=360 equation:

x(x+1)-47x=360

We move all terms to the left:

x(x+1)-47x-(360)=0

We add all the numbers together, and all the variables

-47x+x(x+1)-360=0

We multiply parentheses

x^2-47x+x-360=0

We add all the numbers together, and all the variables

x^2-46x-360=0

a = 1; b = -46; c = -360;
Δ = b2-4ac
Δ = -462-4·1·(-360)
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{889}}{2*1}=\frac{46-2\sqrt{889}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{889}}{2*1}=\frac{46+2\sqrt{889}}{2}
$