4/7*n=22

Solution for 4/7*n=22 equation:

4/7*n=22

We move all terms to the left:

4/7*n-(22)=0


Domain of the equation: 7*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-22*7*n+4=0

Wy multiply elements

-154n*n+4=0

Wy multiply elements

-154n^2+4=0

a = -154; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-154)·4
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{154}}{2*-154}=\frac{0-4\sqrt{154}}{-308}
=-\frac{4\sqrt{154}}{-308}
=-\frac{\sqrt{154}}{-77}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{154}}{2*-154}=\frac{0+4\sqrt{154}}{-308}
=\frac{4\sqrt{154}}{-308}
=\frac{\sqrt{154}}{-77}
$