X^2+3x+42=180

Solution for X^2+3x+42=180 equation:

X^2+3X+42=180

We move all terms to the left:

X^2+3X+42-(180)=0

We add all the numbers together, and all the variables

X^2+3X-138=0

a = 1; b = 3; c = -138;
Δ = b2-4ac
Δ = 32-4·1·(-138)
Δ = 561
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{-(3)-\sqrt{561}}{2*1}=\frac{-3-\sqrt{561}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{561}}{2*1}=\frac{-3+\sqrt{561}}{2}
$