9x^2-24x-17=1

Solution for 9x^2-24x-17=1 equation:

9x^2-24x-17=1

We move all terms to the left:

9x^2-24x-17-(1)=0

We add all the numbers together, and all the variables

9x^2-24x-18=0

a = 9; b = -24; c = -18;
Δ = b2-4ac
Δ = -242-4·9·(-18)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{34}}{2*9}=\frac{24-6\sqrt{34}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{34}}{2*9}=\frac{24+6\sqrt{34}}{18}
$