(u+6)(9u+1)=0

Solution for (u+6)(9u+1)=0 equation:

(u+6)(9u+1)=0

We multiply parentheses ..

(+9u^2+u+54u+6)=0

We get rid of parentheses

9u^2+u+54u+6=0

We add all the numbers together, and all the variables

9u^2+55u+6=0

a = 9; b = 55; c = +6;
Δ = b2-4ac
Δ = 552-4·9·6
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-53}{2*9}=\frac{-108}{18}
=-6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+53}{2*9}=\frac{-2}{18}
=-1/9
$