(x+3)(x+2)=7

Solution for (x+3)(x+2)=7 equation:

(x+3)(x+2)=7

We move all terms to the left:

(x+3)(x+2)-(7)=0

We multiply parentheses ..

(+x^2+2x+3x+6)-7=0

We get rid of parentheses

x^2+2x+3x+6-7=0

We add all the numbers together, and all the variables

x^2+5x-1=0

a = 1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·1·(-1)
Δ = 29
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{-(5)-\sqrt{29}}{2*1}=\frac{-5-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{29}}{2*1}=\frac{-5+\sqrt{29}}{2}
$