X^2-6x+9=75

Solution for X^2-6x+9=75 equation:

X^2-6X+9=75

We move all terms to the left:

X^2-6X+9-(75)=0

We add all the numbers together, and all the variables

X^2-6X-66=0

a = 1; b = -6; c = -66;
Δ = b2-4ac
Δ = -62-4·1·(-66)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{3}}{2*1}=\frac{6-10\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{3}}{2*1}=\frac{6+10\sqrt{3}}{2}
$