X^2+34x-289=0

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

X^2+34X-289=0

a = 1; b = 34; c = -289;
Δ = b2-4ac
Δ = 342-4·1·(-289)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34\sqrt{2}}{2*1}=\frac{-34-34\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34\sqrt{2}}{2*1}=\frac{-34+34\sqrt{2}}{2}
$