4/9*n=10

Solution for 4/9*n=10 equation:

4/9*n=10

We move all terms to the left:

4/9*n-(10)=0


Domain of the equation: 9*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-10*9*n+4=0

Wy multiply elements

-90n*n+4=0

Wy multiply elements

-90n^2+4=0

a = -90; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-90)·4
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-90}=\frac{0-12\sqrt{10}}{-180}
=-\frac{12\sqrt{10}}{-180}
=-\frac{\sqrt{10}}{-15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-90}=\frac{0+12\sqrt{10}}{-180}
=\frac{12\sqrt{10}}{-180}
=\frac{\sqrt{10}}{-15}
$