0=116u^2-274u+20

Solution for 0=116u^2-274u+20 equation:

0=116u^2-274u+20

We move all terms to the left:

0-(116u^2-274u+20)=0

We add all the numbers together, and all the variables

-(116u^2-274u+20)=0

We get rid of parentheses

-116u^2+274u-20=0

a = -116; b = 274; c = -20;
Δ = b2-4ac
Δ = 2742-4·(-116)·(-20)
Δ = 65796
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:

$\sqrt{\Delta}=\sqrt{65796}=\sqrt{4*16449}=\sqrt{4}*\sqrt{16449}=2\sqrt{16449}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(274)-2\sqrt{16449}}{2*-116}=\frac{-274-2\sqrt{16449}}{-232}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(274)+2\sqrt{16449}}{2*-116}=\frac{-274+2\sqrt{16449}}{-232}
$