-16x^2-89x+6=0

Solution for -16x^2-89x+6=0 equation:

-16x^2-89x+6=0

a = -16; b = -89; c = +6;
Δ = b2-4ac
Δ = -892-4·(-16)·6
Δ = 8305
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{-(-89)-\sqrt{8305}}{2*-16}=\frac{89-\sqrt{8305}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{8305}}{2*-16}=\frac{89+\sqrt{8305}}{-32}
$