4n-2n(n-7)=4+3n

Solution for 4n-2n(n-7)=4+3n equation:

4n-2n(n-7)=4+3n

We move all terms to the left:

4n-2n(n-7)-(4+3n)=0

We add all the numbers together, and all the variables

4n-2n(n-7)-(3n+4)=0

We multiply parentheses

-2n^2+4n+14n-(3n+4)=0

We get rid of parentheses

-2n^2+4n+14n-3n-4=0

We add all the numbers together, and all the variables

-2n^2+15n-4=0

a = -2; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·(-2)·(-4)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{193}}{2*-2}=\frac{-15-\sqrt{193}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{193}}{2*-2}=\frac{-15+\sqrt{193}}{-4}
$