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X=5/3.X=3/2
We move all terms to the left:
X-(5/3.X)=0
Domain of the equation: 3.X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(+5/3.X)=0
We get rid of parentheses
X-5/3.X=0
We multiply all the terms by the denominator
X*3.X-5=0
Wy multiply elements
3X^2-5=0
a = 3; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·3·(-5)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*3}=\frac{0-2\sqrt{15}}{6} =-\frac{2\sqrt{15}}{6} =-\frac{\sqrt{15}}{3} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*3}=\frac{0+2\sqrt{15}}{6} =\frac{2\sqrt{15}}{6} =\frac{\sqrt{15}}{3} $
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