x^2+17x+61=0

Solution for x^2+17x+61=0 equation:

x^2+17x+61=0

a = 1; b = 17; c = +61;
Δ = b2-4ac
Δ = 172-4·1·61
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{5}}{2*1}=\frac{-17-3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{5}}{2*1}=\frac{-17+3\sqrt{5}}{2}
$