(2u-1)(6+u)=0

Solution for (2u-1)(6+u)=0 equation:

(2u-1)(6+u)=0

We add all the numbers together, and all the variables

(2u-1)(u+6)=0

We multiply parentheses ..

(+2u^2+12u-1u-6)=0

We get rid of parentheses

2u^2+12u-1u-6=0

We add all the numbers together, and all the variables

2u^2+11u-6=0

a = 2; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·2·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*2}=\frac{-24}{4}
=-6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*2}=\frac{2}{4}
=1/2
$