(x+2)(x+5)=3x+7

Solution for (x+2)(x+5)=3x+7 equation:

(x+2)(x+5)=3x+7

We move all terms to the left:

(x+2)(x+5)-(3x+7)=0

We get rid of parentheses

(x+2)(x+5)-3x-7=0

We multiply parentheses ..

(+x^2+5x+2x+10)-3x-7=0

We get rid of parentheses

x^2+5x+2x-3x+10-7=0

We add all the numbers together, and all the variables

x^2+4x+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$