30x+x^2+40+10x+35=180

Solution for 30x+x^2+40+10x+35=180 equation:

30x+x^2+40+10x+35=180

We move all terms to the left:

30x+x^2+40+10x+35-(180)=0

We add all the numbers together, and all the variables

x^2+40x-105=0

a = 1; b = 40; c = -105;
Δ = b2-4ac
Δ = 402-4·1·(-105)
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{505}}{2*1}=\frac{-40-2\sqrt{505}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{505}}{2*1}=\frac{-40+2\sqrt{505}}{2}
$