(r-2)(r+6)=59

Solution for (r-2)(r+6)=59 equation:

(r-2)(r+6)=59

We move all terms to the left:

(r-2)(r+6)-(59)=0

We multiply parentheses ..

(+r^2+6r-2r-12)-59=0

We get rid of parentheses

r^2+6r-2r-12-59=0

We add all the numbers together, and all the variables

r^2+4r-71=0

a = 1; b = 4; c = -71;
Δ = b2-4ac
Δ = 42-4·1·(-71)
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{3}}{2*1}=\frac{-4-10\sqrt{3}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{3}}{2*1}=\frac{-4+10\sqrt{3}}{2}
$