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5x-2/3x+9=13
We move all terms to the left:
5x-2/3x+9-(13)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
5x-2/3x-4=0
We multiply all the terms by the denominator
5x*3x-4*3x-2=0
Wy multiply elements
15x^2-12x-2=0
a = 15; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·15·(-2)
Δ = 264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*15}=\frac{12-2\sqrt{66}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*15}=\frac{12+2\sqrt{66}}{30} $
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