-16x^2=27x+6

Solution for -16x^2=27x+6 equation:

-16x^2=27x+6

We move all terms to the left:

-16x^2-(27x+6)=0

We get rid of parentheses

-16x^2-27x-6=0

a = -16; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·(-16)·(-6)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{345}}{2*-16}=\frac{27-\sqrt{345}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{345}}{2*-16}=\frac{27+\sqrt{345}}{-32}
$