x(x+19)+66=6

Solution for x(x+19)+66=6 equation:

x(x+19)+66=6

We move all terms to the left:

x(x+19)+66-(6)=0

We add all the numbers together, and all the variables

x(x+19)+60=0

We multiply parentheses

x^2+19x+60=0

a = 1; b = 19; c = +60;
Δ = b2-4ac
Δ = 192-4·1·60
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*1}=\frac{-8}{2}
=-4
$