3r2-26r=16

Solution for 3r2-26r=16 equation:

3r^2-26r=16

We move all terms to the left:

3r^2-26r-(16)=0

a = 3; b = -26; c = -16;
Δ = b2-4ac
Δ = -262-4·3·(-16)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{217}}{2*3}=\frac{26-2\sqrt{217}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{217}}{2*3}=\frac{26+2\sqrt{217}}{6}
$