64x^2-46x+6=0

Solution for 64x^2-46x+6=0 equation:

64x^2-46x+6=0

a = 64; b = -46; c = +6;
Δ = b2-4ac
Δ = -462-4·64·6
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{-(-46)-2\sqrt{145}}{2*64}=\frac{46-2\sqrt{145}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{145}}{2*64}=\frac{46+2\sqrt{145}}{128}
$