x^2-6x=45

Solution for x^2-6x=45 equation:

x^2-6x=45

We move all terms to the left:

x^2-6x-(45)=0

a = 1; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·1·(-45)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{6}}{2*1}=\frac{6-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{6}}{2*1}=\frac{6+6\sqrt{6}}{2}
$