(x+9)(x-4)=6(x+1)

Solution for (x+9)(x-4)=6(x+1) equation:

(x+9)(x-4)=6(x+1)

We move all terms to the left:

(x+9)(x-4)-(6(x+1))=0

We multiply parentheses ..

(+x^2-4x+9x-36)-(6(x+1))=0


We calculate terms in parentheses: -(6(x+1)), so:

6(x+1)

We multiply parentheses

6x+6

Back to the equation:

-(6x+6)


We get rid of parentheses

x^2-4x+9x-6x-36-6=0

We add all the numbers together, and all the variables

x^2-1x-42=0

a = 1; b = -1; c = -42;
Δ = b2-4ac
Δ = -12-4·1·(-42)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*1}=\frac{14}{2}
=7
$