(x+5)(x+2)=44

Solution for (x+5)(x+2)=44 equation:

(x+5)(x+2)=44

We move all terms to the left:

(x+5)(x+2)-(44)=0

We multiply parentheses ..

(+x^2+2x+5x+10)-44=0

We get rid of parentheses

x^2+2x+5x+10-44=0

We add all the numbers together, and all the variables

x^2+7x-34=0

a = 1; b = 7; c = -34;
Δ = b2-4ac
Δ = 72-4·1·(-34)
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{185}}{2*1}=\frac{-7-\sqrt{185}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{185}}{2*1}=\frac{-7+\sqrt{185}}{2}
$