16r+2r^2=54

Solution for 16r+2r^2=54 equation:

16r+2r^2=54

We move all terms to the left:

16r+2r^2-(54)=0

a = 2; b = 16; c = -54;
Δ = b2-4ac
Δ = 162-4·2·(-54)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{43}}{2*2}=\frac{-16-4\sqrt{43}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{43}}{2*2}=\frac{-16+4\sqrt{43}}{4}
$