9x2+18x-47=9

Solution for 9x2+18x-47=9 equation:

9x^2+18x-47=9

We move all terms to the left:

9x^2+18x-47-(9)=0

We add all the numbers together, and all the variables

9x^2+18x-56=0

a = 9; b = 18; c = -56;
Δ = b2-4ac
Δ = 182-4·9·(-56)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{65}}{2*9}=\frac{-18-6\sqrt{65}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{65}}{2*9}=\frac{-18+6\sqrt{65}}{18}
$