X(x+8)+1=62

Solution for X(x+8)+1=62 equation:

X(X+8)+1=62

We move all terms to the left:

X(X+8)+1-(62)=0

We add all the numbers together, and all the variables

X(X+8)-61=0

We multiply parentheses

X^2+8X-61=0

a = 1; b = 8; c = -61;
Δ = b2-4ac
Δ = 82-4·1·(-61)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{77}}{2*1}=\frac{-8-2\sqrt{77}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{77}}{2*1}=\frac{-8+2\sqrt{77}}{2}
$