64x^2-233x+196=0

Solution for 64x^2-233x+196=0 equation:

64x^2-233x+196=0

a = 64; b = -233; c = +196;
Δ = b2-4ac
Δ = -2332-4·64·196
Δ = 4113
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:

$\sqrt{\Delta}=\sqrt{4113}=\sqrt{9*457}=\sqrt{9}*\sqrt{457}=3\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-233)-3\sqrt{457}}{2*64}=\frac{233-3\sqrt{457}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-233)+3\sqrt{457}}{2*64}=\frac{233+3\sqrt{457}}{128}
$