5=(9-6x)*(-x-1)

Solution for 5=(9-6x)*(-x-1) equation:

5=(9-6x)(-x-1)

We move all terms to the left:

5-((9-6x)(-x-1))=0

We add all the numbers together, and all the variables

-((-6x+9)(-1x-1))+5=0

We multiply parentheses ..

-((+6x^2+6x-9x-9))+5=0


We calculate terms in parentheses: -((+6x^2+6x-9x-9)), so:

(+6x^2+6x-9x-9)

We get rid of parentheses

6x^2+6x-9x-9

We add all the numbers together, and all the variables

6x^2-3x-9

Back to the equation:

-(6x^2-3x-9)


We get rid of parentheses

-6x^2+3x+9+5=0

We add all the numbers together, and all the variables

-6x^2+3x+14=0

a = -6; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-6)·14
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{345}}{2*-6}=\frac{-3-\sqrt{345}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*-6}=\frac{-3+\sqrt{345}}{-12}
$