-16x^2+90x-14=0

Solution for -16x^2+90x-14=0 equation:

-16x^2+90x-14=0

a = -16; b = 90; c = -14;
Δ = b2-4ac
Δ = 902-4·(-16)·(-14)
Δ = 7204
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:

$\sqrt{\Delta}=\sqrt{7204}=\sqrt{4*1801}=\sqrt{4}*\sqrt{1801}=2\sqrt{1801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{1801}}{2*-16}=\frac{-90-2\sqrt{1801}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{1801}}{2*-16}=\frac{-90+2\sqrt{1801}}{-32}
$