X+x^2+4x=39

Solution for X+x^2+4x=39 equation:

X+X^2+4X=39

We move all terms to the left:

X+X^2+4X-(39)=0

We add all the numbers together, and all the variables

X^2+5X-39=0

a = 1; b = 5; c = -39;
Δ = b2-4ac
Δ = 52-4·1·(-39)
Δ = 181
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{-(5)-\sqrt{181}}{2*1}=\frac{-5-\sqrt{181}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{181}}{2*1}=\frac{-5+\sqrt{181}}{2}
$