16x^2-84x+92=0

Solution for 16x^2-84x+92=0 equation:

16x^2-84x+92=0

a = 16; b = -84; c = +92;
Δ = b2-4ac
Δ = -842-4·16·92
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{73}}{2*16}=\frac{84-4\sqrt{73}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{73}}{2*16}=\frac{84+4\sqrt{73}}{32}
$