X(6+x)=48

Solution for X(6+x)=48 equation:

X(6+X)=48

We move all terms to the left:

X(6+X)-(48)=0

We add all the numbers together, and all the variables

X(X+6)-48=0

We multiply parentheses

X^2+6X-48=0

a = 1; b = 6; c = -48;
Δ = b2-4ac
Δ = 62-4·1·(-48)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*1}=\frac{-6-2\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*1}=\frac{-6+2\sqrt{57}}{2}
$