x(-2x+9)=-6

Solution for x(-2x+9)=-6 equation:

x(-2x+9)=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

a = -2; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·(-2)·6
Δ = 129
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{-(9)-\sqrt{129}}{2*-2}=\frac{-9-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*-2}=\frac{-9+\sqrt{129}}{-4}
$