16x^2-78x+32=0

Solution for 16x^2-78x+32=0 equation:

16x^2-78x+32=0

a = 16; b = -78; c = +32;
Δ = b2-4ac
Δ = -782-4·16·32
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1009}}{2*16}=\frac{78-2\sqrt{1009}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1009}}{2*16}=\frac{78+2\sqrt{1009}}{32}
$