(-38x+18-16x^2-16x-21)=0

Solution for (-38x+18-16x^2-16x-21)=0 equation:

(-38x+18-16x^2-16x-21)=0

We get rid of parentheses

-16x^2-38x-16x+18-21=0

We add all the numbers together, and all the variables

-16x^2-54x-3=0

a = -16; b = -54; c = -3;
Δ = b2-4ac
Δ = -542-4·(-16)·(-3)
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{681}}{2*-16}=\frac{54-2\sqrt{681}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{681}}{2*-16}=\frac{54+2\sqrt{681}}{-32}
$