-16x^2+30x-5=0

Solution for -16x^2+30x-5=0 equation:

-16x^2+30x-5=0

a = -16; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·(-16)·(-5)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{145}}{2*-16}=\frac{-30-2\sqrt{145}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{145}}{2*-16}=\frac{-30+2\sqrt{145}}{-32}
$