(-x-9)(3x+7)=0

Solution for (-x-9)(3x+7)=0 equation:

(-x-9)(3x+7)=0

We add all the numbers together, and all the variables

(-1x-9)(3x+7)=0

We multiply parentheses ..

(-3x^2-7x-27x-63)=0

We get rid of parentheses

-3x^2-7x-27x-63=0

We add all the numbers together, and all the variables

-3x^2-34x-63=0

a = -3; b = -34; c = -63;
Δ = b2-4ac
Δ = -342-4·(-3)·(-63)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-20}{2*-3}=\frac{14}{-6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+20}{2*-3}=\frac{54}{-6}
=-9
$