(X+5)(x+2)=24+^

Solution for (X+5)(x+2)=24+^ equation:

(X+5)(X+2)=24+^

We move all terms to the left:

(X+5)(X+2)-(24+^)=0

We add all the numbers together, and all the variables

(X+5)(X+2)=0

We multiply parentheses ..

(+X^2+2X+5X+10)=0

We get rid of parentheses

X^2+2X+5X+10=0

We add all the numbers together, and all the variables

X^2+7X+10=0

a = 1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*1}=\frac{-4}{2}
=-2
$