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3x-2/5x=30-4
We move all terms to the left:
3x-2/5x-(30-4)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
3x-2/5x-26=0
We multiply all the terms by the denominator
3x*5x-26*5x-2=0
Wy multiply elements
15x^2-130x-2=0
a = 15; b = -130; c = -2;
Δ = b2-4ac
Δ = -1302-4·15·(-2)
Δ = 17020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17020}=\sqrt{4*4255}=\sqrt{4}*\sqrt{4255}=2\sqrt{4255}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4255}}{2*15}=\frac{130-2\sqrt{4255}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4255}}{2*15}=\frac{130+2\sqrt{4255}}{30} $
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