7/2*n=1

Solution for 7/2*n=1 equation:

7/2*n=1

We move all terms to the left:

7/2*n-(1)=0


Domain of the equation: 2*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-1*2*n+7=0

Wy multiply elements

-2n*n+7=0

Wy multiply elements

-2n^2+7=0

a = -2; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2)·7
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-2}=\frac{0-2\sqrt{14}}{-4}
=-\frac{2\sqrt{14}}{-4}
=-\frac{\sqrt{14}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-2}=\frac{0+2\sqrt{14}}{-4}
=\frac{2\sqrt{14}}{-4}
=\frac{\sqrt{14}}{-2}
$