X(x+8)=45

Solution for X(x+8)=45 equation:

X(X+8)=45

We move all terms to the left:

X(X+8)-(45)=0

We multiply parentheses

X^2+8X-45=0

a = 1; b = 8; c = -45;
Δ = b2-4ac
Δ = 82-4·1·(-45)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{61}}{2*1}=\frac{-8-2\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{61}}{2*1}=\frac{-8+2\sqrt{61}}{2}
$