-16x^2+54x+290=0

Solution for -16x^2+54x+290=0 equation:

-16x^2+54x+290=0

a = -16; b = 54; c = +290;
Δ = b2-4ac
Δ = 542-4·(-16)·290
Δ = 21476
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:

$\sqrt{\Delta}=\sqrt{21476}=\sqrt{4*5369}=\sqrt{4}*\sqrt{5369}=2\sqrt{5369}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{5369}}{2*-16}=\frac{-54-2\sqrt{5369}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{5369}}{2*-16}=\frac{-54+2\sqrt{5369}}{-32}
$