2x^2-52x-34=0

Solution for 2x^2-52x-34=0 equation:

2x^2-52x-34=0

a = 2; b = -52; c = -34;
Δ = b2-4ac
Δ = -522-4·2·(-34)
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{186}}{2*2}=\frac{52-4\sqrt{186}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{186}}{2*2}=\frac{52+4\sqrt{186}}{4}
$