(x+17)(x+17)=19

Solution for (x+17)(x+17)=19 equation:

(x+17)(x+17)=19

We move all terms to the left:

(x+17)(x+17)-(19)=0

We multiply parentheses ..

(+x^2+17x+17x+289)-19=0

We get rid of parentheses

x^2+17x+17x+289-19=0

We add all the numbers together, and all the variables

x^2+34x+270=0

a = 1; b = 34; c = +270;
Δ = b2-4ac
Δ = 342-4·1·270
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{19}}{2*1}=\frac{-34-2\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{19}}{2*1}=\frac{-34+2\sqrt{19}}{2}
$