6r^2-38r=16

Solution for 6r^2-38r=16 equation:

6r^2-38r=16

We move all terms to the left:

6r^2-38r-(16)=0

a = 6; b = -38; c = -16;
Δ = b2-4ac
Δ = -382-4·6·(-16)
Δ = 1828
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:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{457}}{2*6}=\frac{38-2\sqrt{457}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{457}}{2*6}=\frac{38+2\sqrt{457}}{12}
$