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11x+2=11/15x+5
We move all terms to the left:
11x+2-(11/15x+5)=0
Domain of the equation: 15x+5)!=0We get rid of parentheses
x∈R
11x-11/15x-5+2=0
We multiply all the terms by the denominator
11x*15x-5*15x+2*15x-11=0
Wy multiply elements
165x^2-75x+30x-11=0
We add all the numbers together, and all the variables
165x^2-45x-11=0
a = 165; b = -45; c = -11;
Δ = b2-4ac
Δ = -452-4·165·(-11)
Δ = 9285
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{-(-45)-\sqrt{9285}}{2*165}=\frac{45-\sqrt{9285}}{330} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{9285}}{2*165}=\frac{45+\sqrt{9285}}{330} $
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