0=(u^2)-6u-7

Solution for 0=(u^2)-6u-7 equation:

0=(u^2)-6u-7

We move all terms to the left:

0-((u^2)-6u-7)=0

We add all the numbers together, and all the variables

-(u^2-6u-7)=0

We get rid of parentheses

-u^2+6u+7=0

We add all the numbers together, and all the variables

-1u^2+6u+7=0

a = -1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-1)·7
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8}{2*-1}=\frac{-14}{-2}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8}{2*-1}=\frac{2}{-2}
=-1
$