8x^2-18x-5=9

Solution for 8x^2-18x-5=9 equation:

8x^2-18x-5=9

We move all terms to the left:

8x^2-18x-5-(9)=0

We add all the numbers together, and all the variables

8x^2-18x-14=0

a = 8; b = -18; c = -14;
Δ = b2-4ac
Δ = -182-4·8·(-14)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{193}}{2*8}=\frac{18-2\sqrt{193}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{193}}{2*8}=\frac{18+2\sqrt{193}}{16}
$