x^2+6x-17=180

Solution for x^2+6x-17=180 equation:

x^2+6x-17=180

We move all terms to the left:

x^2+6x-17-(180)=0

We add all the numbers together, and all the variables

x^2+6x-197=0

a = 1; b = 6; c = -197;
Δ = b2-4ac
Δ = 62-4·1·(-197)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{206}}{2*1}=\frac{-6-2\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{206}}{2*1}=\frac{-6+2\sqrt{206}}{2}
$