16x^2-18x-9=9

Solution for 16x^2-18x-9=9 equation:

16x^2-18x-9=9

We move all terms to the left:

16x^2-18x-9-(9)=0

We add all the numbers together, and all the variables

16x^2-18x-18=0

a = 16; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·16·(-18)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{41}}{2*16}=\frac{18-6\sqrt{41}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{41}}{2*16}=\frac{18+6\sqrt{41}}{32}
$