9x^2-30x-32=0

Solution for 9x^2-30x-32=0 equation:

9x^2-30x-32=0

a = 9; b = -30; c = -32;
Δ = b2-4ac
Δ = -302-4·9·(-32)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{57}}{2*9}=\frac{30-6\sqrt{57}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{57}}{2*9}=\frac{30+6\sqrt{57}}{18}
$