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5/3x-2=x+6
We move all terms to the left:
5/3x-2-(x+6)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
5/3x-x-6-2=0
We multiply all the terms by the denominator
-x*3x-6*3x-2*3x+5=0
Wy multiply elements
-3x^2-18x-6x+5=0
We add all the numbers together, and all the variables
-3x^2-24x+5=0
a = -3; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·(-3)·5
Δ = 636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{159}}{2*-3}=\frac{24-2\sqrt{159}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{159}}{2*-3}=\frac{24+2\sqrt{159}}{-6} $
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