(x+9)(-7x-8)=0

Solution for (x+9)(-7x-8)=0 equation:

(x+9)(-7x-8)=0

We multiply parentheses ..

(-7x^2-8x-63x-72)=0

We get rid of parentheses

-7x^2-8x-63x-72=0

We add all the numbers together, and all the variables

-7x^2-71x-72=0

a = -7; b = -71; c = -72;
Δ = b2-4ac
Δ = -712-4·(-7)·(-72)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-55}{2*-7}=\frac{16}{-14}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+55}{2*-7}=\frac{126}{-14}
=-9
$