6u^2-37u+6=0

Solution for 6u^2-37u+6=0 equation:

6u^2-37u+6=0

a = 6; b = -37; c = +6;
Δ = b2-4ac
Δ = -372-4·6·6
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-35}{2*6}=\frac{2}{12}
=1/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+35}{2*6}=\frac{72}{12}
=6
$