(4n-2)(7-n)=

Solution for (4n-2)(7-n)= equation:

(4n-2)(7-n)=

We move all terms to the left:

(4n-2)(7-n)-()=0

We add all the numbers together, and all the variables

(4n-2)(-1n+7)-()=0

We add all the numbers together, and all the variables

(4n-2)(-1n+7)=0

We multiply parentheses ..

(-4n^2+28n+2n-14)=0

We get rid of parentheses

-4n^2+28n+2n-14=0

We add all the numbers together, and all the variables

-4n^2+30n-14=0

a = -4; b = 30; c = -14;
Δ = b2-4ac
Δ = 302-4·(-4)·(-14)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-26}{2*-4}=\frac{-56}{-8}
=+7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+26}{2*-4}=\frac{-4}{-8}
=1/2
$