4/7*n=14

Solution for 4/7*n=14 equation:

4/7*n=14

We move all terms to the left:

4/7*n-(14)=0


Domain of the equation: 7*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-14*7*n+4=0

Wy multiply elements

-98n*n+4=0

Wy multiply elements

-98n^2+4=0

a = -98; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-98)·4
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*-98}=\frac{0-28\sqrt{2}}{-196}
=-\frac{28\sqrt{2}}{-196}
=-\frac{\sqrt{2}}{-7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*-98}=\frac{0+28\sqrt{2}}{-196}
=\frac{28\sqrt{2}}{-196}
=\frac{\sqrt{2}}{-7}
$