(x+2)(x+5)=46

Solution for (x+2)(x+5)=46 equation:

(x+2)(x+5)=46

We move all terms to the left:

(x+2)(x+5)-(46)=0

We multiply parentheses ..

(+x^2+5x+2x+10)-46=0

We get rid of parentheses

x^2+5x+2x+10-46=0

We add all the numbers together, and all the variables

x^2+7x-36=0

a = 1; b = 7; c = -36;
Δ = b2-4ac
Δ = 72-4·1·(-36)
Δ = 193
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{193}}{2*1}=\frac{-7-\sqrt{193}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{193}}{2*1}=\frac{-7+\sqrt{193}}{2}
$