x(x+40)+30=180

Solution for x(x+40)+30=180 equation:

x(x+40)+30=180

We move all terms to the left:

x(x+40)+30-(180)=0

We add all the numbers together, and all the variables

x(x+40)-150=0

We multiply parentheses

x^2+40x-150=0

a = 1; b = 40; c = -150;
Δ = b2-4ac
Δ = 402-4·1·(-150)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{22}}{2*1}=\frac{-40-10\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{22}}{2*1}=\frac{-40+10\sqrt{22}}{2}
$