32x^2-58x+8=0

Solution for 32x^2-58x+8=0 equation:

32x^2-58x+8=0

a = 32; b = -58; c = +8;
Δ = b2-4ac
Δ = -582-4·32·8
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-6\sqrt{65}}{2*32}=\frac{58-6\sqrt{65}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+6\sqrt{65}}{2*32}=\frac{58+6\sqrt{65}}{64}
$