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5x-11=-2/3x+6
We move all terms to the left:
5x-11-(-2/3x+6)=0
Domain of the equation: 3x+6)!=0We get rid of parentheses
x∈R
5x+2/3x-6-11=0
We multiply all the terms by the denominator
5x*3x-6*3x-11*3x+2=0
Wy multiply elements
15x^2-18x-33x+2=0
We add all the numbers together, and all the variables
15x^2-51x+2=0
a = 15; b = -51; c = +2;
Δ = b2-4ac
Δ = -512-4·15·2
Δ = 2481
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{-(-51)-\sqrt{2481}}{2*15}=\frac{51-\sqrt{2481}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2481}}{2*15}=\frac{51+\sqrt{2481}}{30} $
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