x(x+25)=186

Solution for x(x+25)=186 equation:

x(x+25)=186

We move all terms to the left:

x(x+25)-(186)=0

We multiply parentheses

x^2+25x-186=0

a = 1; b = 25; c = -186;
Δ = b2-4ac
Δ = 252-4·1·(-186)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-37}{2*1}=\frac{-62}{2}
=-31
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+37}{2*1}=\frac{12}{2}
=6
$