2x^2-32x+13=0

Solution for 2x^2-32x+13=0 equation:

2x^2-32x+13=0

a = 2; b = -32; c = +13;
Δ = b2-4ac
Δ = -322-4·2·13
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{230}}{2*2}=\frac{32-2\sqrt{230}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{230}}{2*2}=\frac{32+2\sqrt{230}}{4}
$