64x^2+30x+1=0

Solution for 64x^2+30x+1=0 equation:

64x^2+30x+1=0

a = 64; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·64·1
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{161}}{2*64}=\frac{-30-2\sqrt{161}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{161}}{2*64}=\frac{-30+2\sqrt{161}}{128}
$