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1/5x-2/3x-2=2/5x
We move all terms to the left:
1/5x-2/3x-2-(2/5x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/5x-2/3x-(+2/5x)-2=0
We get rid of parentheses
1/5x-2/3x-2/5x-2=0
We calculate fractions
(-6x+1)/15x^2+(-10x)/15x^2-2=0
We multiply all the terms by the denominator
(-6x+1)+(-10x)-2*15x^2=0
Wy multiply elements
-30x^2+(-6x+1)+(-10x)=0
We get rid of parentheses
-30x^2-6x-10x+1=0
We add all the numbers together, and all the variables
-30x^2-16x+1=0
a = -30; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-30)·1
Δ = 376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{94}}{2*-30}=\frac{16-2\sqrt{94}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{94}}{2*-30}=\frac{16+2\sqrt{94}}{-60} $
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