2x2-13x+2=0

Solution for 2x2-13x+2=0 equation:

2x^2-13x+2=0

a = 2; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·2·2
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{17}}{2*2}=\frac{13-3\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{17}}{2*2}=\frac{13+3\sqrt{17}}{4}
$