-16x2+46x-20=0

Solution for -16x2+46x-20=0 equation:

-16x^2+46x-20=0

a = -16; b = 46; c = -20;
Δ = b2-4ac
Δ = 462-4·(-16)·(-20)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{209}}{2*-16}=\frac{-46-2\sqrt{209}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{209}}{2*-16}=\frac{-46+2\sqrt{209}}{-32}
$