9(x^2)-15x-16=0

Solution for 9(x^2)-15x-16=0 equation:

9(x^2)-15x-16=0

a = 9; b = -15; c = -16;
Δ = b2-4ac
Δ = -152-4·9·(-16)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{89}}{2*9}=\frac{15-3\sqrt{89}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{89}}{2*9}=\frac{15+3\sqrt{89}}{18}
$