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

Solution for 5(u-7)-2u(u-7)=0 equation:

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

We multiply parentheses

-2u^2+5u+14u-35=0

We add all the numbers together, and all the variables

-2u^2+19u-35=0

a = -2; b = 19; c = -35;
Δ = b2-4ac
Δ = 192-4·(-2)·(-35)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-9}{2*-2}=\frac{-28}{-4}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+9}{2*-2}=\frac{-10}{-4}
=2+1/2
$