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X=8/3X+17
We move all terms to the left:
X-(8/3X+17)=0
Domain of the equation: 3X+17)!=0We get rid of parentheses
X∈R
X-8/3X-17=0
We multiply all the terms by the denominator
X*3X-17*3X-8=0
Wy multiply elements
3X^2-51X-8=0
a = 3; b = -51; c = -8;
Δ = b2-4ac
Δ = -512-4·3·(-8)
Δ = 2697
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{2697}}{2*3}=\frac{51-\sqrt{2697}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2697}}{2*3}=\frac{51+\sqrt{2697}}{6} $
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