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6x-7=2/3x+2
We move all terms to the left:
6x-7-(2/3x+2)=0
Domain of the equation: 3x+2)!=0We get rid of parentheses
x∈R
6x-2/3x-2-7=0
We multiply all the terms by the denominator
6x*3x-2*3x-7*3x-2=0
Wy multiply elements
18x^2-6x-21x-2=0
We add all the numbers together, and all the variables
18x^2-27x-2=0
a = 18; b = -27; c = -2;
Δ = b2-4ac
Δ = -272-4·18·(-2)
Δ = 873
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{97}}{2*18}=\frac{27-3\sqrt{97}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{97}}{2*18}=\frac{27+3\sqrt{97}}{36} $
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