X*x+X+42=180

Solution for X*x+X+42=180 equation:

X*X+X+42=180

We move all terms to the left:

X*X+X+42-(180)=0

We add all the numbers together, and all the variables

X+X*X-138=0

Wy multiply elements

X^2+X-138=0

a = 1; b = 1; c = -138;
Δ = b2-4ac
Δ = 12-4·1·(-138)
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{553}}{2*1}=\frac{-1-\sqrt{553}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{553}}{2*1}=\frac{-1+\sqrt{553}}{2}
$