(7-u)(2u-1)=0

Solution for (7-u)(2u-1)=0 equation:

(7-u)(2u-1)=0

We add all the numbers together, and all the variables

(-1u+7)(2u-1)=0

We multiply parentheses ..

(-2u^2+u+14u-7)=0

We get rid of parentheses

-2u^2+u+14u-7=0

We add all the numbers together, and all the variables

-2u^2+15u-7=0

a = -2; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·(-2)·(-7)
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{-(15)-13}{2*-2}=\frac{-28}{-4}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*-2}=\frac{-2}{-4}
=1/2
$