(x-9)(x+4)=3(56)

Solution for (x-9)(x+4)=3(56) equation:

(x-9)(x+4)=3(56)

We move all terms to the left:

(x-9)(x+4)-(3(56))=0

determiningTheFunctionDomain
(x-9)(x+4)-356=0

We multiply parentheses ..

(+x^2+4x-9x-36)-356=0

We get rid of parentheses

x^2+4x-9x-36-356=0

We add all the numbers together, and all the variables

x^2-5x-392=0

a = 1; b = -5; c = -392;
Δ = b2-4ac
Δ = -52-4·1·(-392)
Δ = 1593
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{177}}{2*1}=\frac{5-3\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{177}}{2*1}=\frac{5+3\sqrt{177}}{2}
$