2x^2-34x-289=0

Solution for 2x^2-34x-289=0 equation:

2x^2-34x-289=0

a = 2; b = -34; c = -289;
Δ = b2-4ac
Δ = -342-4·2·(-289)
Δ = 3468
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:

$\sqrt{\Delta}=\sqrt{3468}=\sqrt{1156*3}=\sqrt{1156}*\sqrt{3}=34\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34\sqrt{3}}{2*2}=\frac{34-34\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34\sqrt{3}}{2*2}=\frac{34+34\sqrt{3}}{4}
$