9p^2-18p-34=8

Solution for 9p^2-18p-34=8 equation:

9p^2-18p-34=8

We move all terms to the left:

9p^2-18p-34-(8)=0

We add all the numbers together, and all the variables

9p^2-18p-42=0

a = 9; b = -18; c = -42;
Δ = b2-4ac
Δ = -182-4·9·(-42)
Δ = 1836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{51}}{2*9}=\frac{18-6\sqrt{51}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{51}}{2*9}=\frac{18+6\sqrt{51}}{18}
$