(x+7)(-x+3)=24

Solution for (x+7)(-x+3)=24 equation:

(x+7)(-x+3)=24

We move all terms to the left:

(x+7)(-x+3)-(24)=0

We add all the numbers together, and all the variables

(x+7)(-1x+3)-24=0

We multiply parentheses ..

(-1x^2+3x-7x+21)-24=0

We get rid of parentheses

-1x^2+3x-7x+21-24=0

We add all the numbers together, and all the variables

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