x^2+x+29=180

Solution for x^2+x+29=180 equation:

x^2+x+29=180

We move all terms to the left:

x^2+x+29-(180)=0

We add all the numbers together, and all the variables

x^2+x-151=0

a = 1; b = 1; c = -151;
Δ = b2-4ac
Δ = 12-4·1·(-151)
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11\sqrt{5}}{2*1}=\frac{-1-11\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11\sqrt{5}}{2*1}=\frac{-1+11\sqrt{5}}{2}
$