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x+34-5=2/3x+6
We move all terms to the left:
x+34-5-(2/3x+6)=0
Domain of the equation: 3x+6)!=0We add all the numbers together, and all the variables
x∈R
x-(2/3x+6)+29=0
We get rid of parentheses
x-2/3x-6+29=0
We multiply all the terms by the denominator
x*3x-6*3x+29*3x-2=0
Wy multiply elements
3x^2-18x+87x-2=0
We add all the numbers together, and all the variables
3x^2+69x-2=0
a = 3; b = 69; c = -2;
Δ = b2-4ac
Δ = 692-4·3·(-2)
Δ = 4785
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{-(69)-\sqrt{4785}}{2*3}=\frac{-69-\sqrt{4785}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{4785}}{2*3}=\frac{-69+\sqrt{4785}}{6} $
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