X(x+14)=262

Solution for X(x+14)=262 equation:

X(X+14)=262

We move all terms to the left:

X(X+14)-(262)=0

We multiply parentheses

X^2+14X-262=0

a = 1; b = 14; c = -262;
Δ = b2-4ac
Δ = 142-4·1·(-262)
Δ = 1244
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:

$\sqrt{\Delta}=\sqrt{1244}=\sqrt{4*311}=\sqrt{4}*\sqrt{311}=2\sqrt{311}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{311}}{2*1}=\frac{-14-2\sqrt{311}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{311}}{2*1}=\frac{-14+2\sqrt{311}}{2}
$