-2x(x-9)-29=-11

Solution for -2x(x-9)-29=-11 equation:

-2x(x-9)-29=-11

We move all terms to the left:

-2x(x-9)-29-(-11)=0

We add all the numbers together, and all the variables

-2x(x-9)-18=0

We multiply parentheses

-2x^2+18x-18=0

a = -2; b = 18; c = -18;
Δ = b2-4ac
Δ = 182-4·(-2)·(-18)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{5}}{2*-2}=\frac{-18-6\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{5}}{2*-2}=\frac{-18+6\sqrt{5}}{-4}
$