r^2-16r=43

Solution for r^2-16r=43 equation:

r^2-16r=43

We move all terms to the left:

r^2-16r-(43)=0

a = 1; b = -16; c = -43;
Δ = b2-4ac
Δ = -162-4·1·(-43)
Δ = 428
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:

$\sqrt{\Delta}=\sqrt{428}=\sqrt{4*107}=\sqrt{4}*\sqrt{107}=2\sqrt{107}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{107}}{2*1}=\frac{16-2\sqrt{107}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{107}}{2*1}=\frac{16+2\sqrt{107}}{2}
$