(X+17)(x+7)=-4

Solution for (X+17)(x+7)=-4 equation:

(X+17)(X+7)=-4

We move all terms to the left:

(X+17)(X+7)-(-4)=0

We add all the numbers together, and all the variables

(X+17)(X+7)+4=0

We multiply parentheses ..

(+X^2+7X+17X+119)+4=0

We get rid of parentheses

X^2+7X+17X+119+4=0

We add all the numbers together, and all the variables

X^2+24X+123=0

a = 1; b = 24; c = +123;
Δ = b2-4ac
Δ = 242-4·1·123
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{21}}{2*1}=\frac{-24-2\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{21}}{2*1}=\frac{-24+2\sqrt{21}}{2}
$