(4u+1)(7-u)=0

Solution for (4u+1)(7-u)=0 equation:

(4u+1)(7-u)=0

We add all the numbers together, and all the variables

(4u+1)(-1u+7)=0

We multiply parentheses ..

(-4u^2+28u-1u+7)=0

We get rid of parentheses

-4u^2+28u-1u+7=0

We add all the numbers together, and all the variables

-4u^2+27u+7=0

a = -4; b = 27; c = +7;
Δ = b2-4ac
Δ = 272-4·(-4)·7
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-29}{2*-4}=\frac{-56}{-8}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+29}{2*-4}=\frac{2}{-8}
=-1/4
$