42-5/4n=4n

Solution for 42-5/4n=4n equation:

42-5/4n=4n

We move all terms to the left:

42-5/4n-(4n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-4n-5/4n+42=0

We multiply all the terms by the denominator


-4n*4n+42*4n-5=0

Wy multiply elements

-16n^2+168n-5=0

a = -16; b = 168; c = -5;
Δ = b2-4ac
Δ = 1682-4·(-16)·(-5)
Δ = 27904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27904}=\sqrt{256*109}=\sqrt{256}*\sqrt{109}=16\sqrt{109}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-16\sqrt{109}}{2*-16}=\frac{-168-16\sqrt{109}}{-32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+16\sqrt{109}}{2*-16}=\frac{-168+16\sqrt{109}}{-32}
$