X(x+5)=38

Solution for X(x+5)=38 equation:

X(X+5)=38

We move all terms to the left:

X(X+5)-(38)=0

We multiply parentheses

X^2+5X-38=0

a = 1; b = 5; c = -38;
Δ = b2-4ac
Δ = 52-4·1·(-38)
Δ = 177
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{177}}{2*1}=\frac{-5-\sqrt{177}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{177}}{2*1}=\frac{-5+\sqrt{177}}{2}
$