X(x+4)=140^2

Solution for X(x+4)=140^2 equation:

X(X+4)=140^2

We move all terms to the left:

X(X+4)-(140^2)=0

We add all the numbers together, and all the variables

X(X+4)-19600=0

We multiply parentheses

X^2+4X-19600=0

a = 1; b = 4; c = -19600;
Δ = b2-4ac
Δ = 42-4·1·(-19600)
Δ = 78416
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:

$\sqrt{\Delta}=\sqrt{78416}=\sqrt{2704*29}=\sqrt{2704}*\sqrt{29}=52\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-52\sqrt{29}}{2*1}=\frac{-4-52\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+52\sqrt{29}}{2*1}=\frac{-4+52\sqrt{29}}{2}
$