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x=13-1/3x+4
We move all terms to the left:
x-(13-1/3x+4)=0
Domain of the equation: 3x+4)!=0We add all the numbers together, and all the variables
x∈R
x-(-1/3x+17)=0
We get rid of parentheses
x+1/3x-17=0
We multiply all the terms by the denominator
x*3x-17*3x+1=0
Wy multiply elements
3x^2-51x+1=0
a = 3; b = -51; c = +1;
Δ = b2-4ac
Δ = -512-4·3·1
Δ = 2589
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{2589}}{2*3}=\frac{51-\sqrt{2589}}{6}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2589}}{2*3}=\frac{51+\sqrt{2589}}{6}
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