6u^2-11u=72

Solution for 6u^2-11u=72 equation:

6u^2-11u=72

We move all terms to the left:

6u^2-11u-(72)=0

a = 6; b = -11; c = -72;
Δ = b2-4ac
Δ = -112-4·6·(-72)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-43}{2*6}=\frac{-32}{12}
=-2+2/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+43}{2*6}=\frac{54}{12}
=4+1/2
$