0=9x^2-4x-16

Solution for 0=9x^2-4x-16 equation:

0=9x^2-4x-16

We move all terms to the left:

0-(9x^2-4x-16)=0

We add all the numbers together, and all the variables

-(9x^2-4x-16)=0

We get rid of parentheses

-9x^2+4x+16=0

a = -9; b = 4; c = +16;
Δ = b2-4ac
Δ = 42-4·(-9)·16
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{37}}{2*-9}=\frac{-4-4\sqrt{37}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{37}}{2*-9}=\frac{-4+4\sqrt{37}}{-18}
$