x^2+4+x+30=180

Solution for x^2+4+x+30=180 equation:

x^2+4+x+30=180

We move all terms to the left:

x^2+4+x+30-(180)=0

We add all the numbers together, and all the variables

x^2+x-146=0

a = 1; b = 1; c = -146;
Δ = b2-4ac
Δ = 12-4·1·(-146)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{65}}{2*1}=\frac{-1-3\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{65}}{2*1}=\frac{-1+3\sqrt{65}}{2}
$