x2-4x-45=8

Solution for x2-4x-45=8 equation:

x2-4x-45=8

We move all terms to the left:

x2-4x-45-(8)=0

We add all the numbers together, and all the variables

x^2-4x-53=0

a = 1; b = -4; c = -53;
Δ = b2-4ac
Δ = -42-4·1·(-53)
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{-(-4)-2\sqrt{57}}{2*1}=\frac{4-2\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{57}}{2*1}=\frac{4+2\sqrt{57}}{2}
$