(X+1)(x+5)=45

Solution for (X+1)(x+5)=45 equation:

(X+1)(X+5)=45

We move all terms to the left:

(X+1)(X+5)-(45)=0

We multiply parentheses ..

(+X^2+5X+X+5)-45=0

We get rid of parentheses

X^2+5X+X+5-45=0

We add all the numbers together, and all the variables

X^2+6X-40=0

a = 1; b = 6; c = -40;
Δ = b2-4ac
Δ = 62-4·1·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*1}=\frac{8}{2}
=4
$