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(2x+3)-(5x-2)/6x+11=2/17
We move all terms to the left:
(2x+3)-(5x-2)/6x+11-(2/17)=0
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
(2x+3)-(5x-2)/6x+11-(+2/17)=0
We get rid of parentheses
2x-(5x-2)/6x+3+11-2/17=0
We calculate fractions
2x+(-85x+34)/102x+(-12x)/102x+3+11=0
We add all the numbers together, and all the variables
2x+(-85x+34)/102x+(-12x)/102x+14=0
We multiply all the terms by the denominator
2x*102x+(-85x+34)+(-12x)+14*102x=0
Wy multiply elements
204x^2+(-85x+34)+(-12x)+1428x=0
We get rid of parentheses
204x^2-85x-12x+1428x+34=0
We add all the numbers together, and all the variables
204x^2+1331x+34=0
a = 204; b = 1331; c = +34;
Δ = b2-4ac
Δ = 13312-4·204·34
Δ = 1743817
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1331)-\sqrt{1743817}}{2*204}=\frac{-1331-\sqrt{1743817}}{408} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1331)+\sqrt{1743817}}{2*204}=\frac{-1331+\sqrt{1743817}}{408} $
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