0=3u^2-2u-7

Solution for 0=3u^2-2u-7 equation:

0=3u^2-2u-7

We move all terms to the left:

0-(3u^2-2u-7)=0

We add all the numbers together, and all the variables

-(3u^2-2u-7)=0

We get rid of parentheses

-3u^2+2u+7=0

a = -3; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-3)·7
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*-3}=\frac{-2-2\sqrt{22}}{-6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*-3}=\frac{-2+2\sqrt{22}}{-6}
$