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(4/9)*n=10
We move all terms to the left:
(4/9)*n-(10)=0
Domain of the equation: 9)*n!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
(+4/9)*n-10=0
We multiply parentheses
4n^2-10=0
a = 4; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·4·(-10)
Δ = 160
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*4}=\frac{0-4\sqrt{10}}{8} =-\frac{4\sqrt{10}}{8} =-\frac{\sqrt{10}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*4}=\frac{0+4\sqrt{10}}{8} =\frac{4\sqrt{10}}{8} =\frac{\sqrt{10}}{2} $
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