21n-6/15n-9=0

Solution for 21n-6/15n-9=0 equation:

21n-6/15n-9=0


Domain of the equation: 15n!=0

n!=0/15

n!=0

n∈R


We multiply all the terms by the denominator


21n*15n-9*15n-6=0

Wy multiply elements

315n^2-135n-6=0

a = 315; b = -135; c = -6;
Δ = b2-4ac
Δ = -1352-4·315·(-6)
Δ = 25785
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:

$\sqrt{\Delta}=\sqrt{25785}=\sqrt{9*2865}=\sqrt{9}*\sqrt{2865}=3\sqrt{2865}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2865}}{2*315}=\frac{135-3\sqrt{2865}}{630}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2865}}{2*315}=\frac{135+3\sqrt{2865}}{630}
$