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x=2/3x-5
We move all terms to the left:
x-(2/3x-5)=0
Domain of the equation: 3x-5)!=0We get rid of parentheses
x∈R
x-2/3x+5=0
We multiply all the terms by the denominator
x*3x+5*3x-2=0
Wy multiply elements
3x^2+15x-2=0
a = 3; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·3·(-2)
Δ = 249
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{-(15)-\sqrt{249}}{2*3}=\frac{-15-\sqrt{249}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*3}=\frac{-15+\sqrt{249}}{6} $
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