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x-7=2/3x-14
We move all terms to the left:
x-7-(2/3x-14)=0
Domain of the equation: 3x-14)!=0We get rid of parentheses
x∈R
x-2/3x+14-7=0
We multiply all the terms by the denominator
x*3x+14*3x-7*3x-2=0
Wy multiply elements
3x^2+42x-21x-2=0
We add all the numbers together, and all the variables
3x^2+21x-2=0
a = 3; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·3·(-2)
Δ = 465
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{-(21)-\sqrt{465}}{2*3}=\frac{-21-\sqrt{465}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{465}}{2*3}=\frac{-21+\sqrt{465}}{6} $
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