x^2+34x-15=0

Solution for x^2+34x-15=0 equation:

x^2+34x-15=0

a = 1; b = 34; c = -15;
Δ = b2-4ac
Δ = 342-4·1·(-15)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-8\sqrt{19}}{2*1}=\frac{-34-8\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+8\sqrt{19}}{2*1}=\frac{-34+8\sqrt{19}}{2}
$