r^2-17=4r

Solution for r^2-17=4r equation:

r^2-17=4r

We move all terms to the left:

r^2-17-(4r)=0

a = 1; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·1·(-17)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{21}}{2*1}=\frac{4-2\sqrt{21}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{21}}{2*1}=\frac{4+2\sqrt{21}}{2}
$