9x^2-3x-5=9

Solution for 9x^2-3x-5=9 equation:

9x^2-3x-5=9

We move all terms to the left:

9x^2-3x-5-(9)=0

We add all the numbers together, and all the variables

9x^2-3x-14=0

a = 9; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·9·(-14)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{57}}{2*9}=\frac{3-3\sqrt{57}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{57}}{2*9}=\frac{3+3\sqrt{57}}{18}
$