(x+17)(x+3)=5^2

Solution for (x+17)(x+3)=5^2 equation:

(x+17)(x+3)=5^2

We move all terms to the left:

(x+17)(x+3)-(5^2)=0

We add all the numbers together, and all the variables

(x+17)(x+3)-25=0

We multiply parentheses ..

(+x^2+3x+17x+51)-25=0

We get rid of parentheses

x^2+3x+17x+51-25=0

We add all the numbers together, and all the variables

x^2+20x+26=0

a = 1; b = 20; c = +26;
Δ = b2-4ac
Δ = 202-4·1·26
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{74}}{2*1}=\frac{-20-2\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{74}}{2*1}=\frac{-20+2\sqrt{74}}{2}
$