x(x+12)=45

Solution for x(x+12)=45 equation:

x(x+12)=45

We move all terms to the left:

x(x+12)-(45)=0

We multiply parentheses

x^2+12x-45=0

a = 1; b = 12; c = -45;
Δ = b2-4ac
Δ = 122-4·1·(-45)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*1}=\frac{6}{2}
=3
$