-16x^2+234x-334=0

Solution for -16x^2+234x-334=0 equation:

-16x^2+234x-334=0

a = -16; b = 234; c = -334;
Δ = b2-4ac
Δ = 2342-4·(-16)·(-334)
Δ = 33380
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:

$\sqrt{\Delta}=\sqrt{33380}=\sqrt{4*8345}=\sqrt{4}*\sqrt{8345}=2\sqrt{8345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{8345}}{2*-16}=\frac{-234-2\sqrt{8345}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{8345}}{2*-16}=\frac{-234+2\sqrt{8345}}{-32}
$