(x-9)(x-3)=30

Solution for (x-9)(x-3)=30 equation:

(x-9)(x-3)=30

We move all terms to the left:

(x-9)(x-3)-(30)=0

We multiply parentheses ..

(+x^2-3x-9x+27)-30=0

We get rid of parentheses

x^2-3x-9x+27-30=0

We add all the numbers together, and all the variables

x^2-12x-3=0

a = 1; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·1·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*1}=\frac{12-2\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*1}=\frac{12+2\sqrt{39}}{2}
$