21/2*n=10

Solution for 21/2*n=10 equation:

21/2*n=10

We move all terms to the left:

21/2*n-(10)=0


Domain of the equation: 2*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-10*2*n+21=0

Wy multiply elements

-20n*n+21=0

Wy multiply elements

-20n^2+21=0

a = -20; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-20)·21
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-20}=\frac{0-4\sqrt{105}}{-40}
=-\frac{4\sqrt{105}}{-40}
=-\frac{\sqrt{105}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-20}=\frac{0+4\sqrt{105}}{-40}
=\frac{4\sqrt{105}}{-40}
=\frac{\sqrt{105}}{-10}
$