(x-8)(x-2)=21

Solution for (x-8)(x-2)=21 equation:

(x-8)(x-2)=21

We move all terms to the left:

(x-8)(x-2)-(21)=0

We multiply parentheses ..

(+x^2-2x-8x+16)-21=0

We get rid of parentheses

x^2-2x-8x+16-21=0

We add all the numbers together, and all the variables

x^2-10x-5=0

a = 1; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·1·(-5)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{30}}{2*1}=\frac{10-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{30}}{2*1}=\frac{10+2\sqrt{30}}{2}
$