2u^2-11u^2+12=0

Solution for 2u^2-11u^2+12=0 equation:

2u^2-11u^2+12=0

We add all the numbers together, and all the variables

-9u^2+12=0

a = -9; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-9)·12
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-9}=\frac{0-12\sqrt{3}}{-18}
=-\frac{12\sqrt{3}}{-18}
=-\frac{2\sqrt{3}}{-3}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-9}=\frac{0+12\sqrt{3}}{-18}
=\frac{12\sqrt{3}}{-18}
=\frac{2\sqrt{3}}{-3}
$