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(-2x-2)-(1/3x+3)=0
Domain of the equation: 3x+3)!=0We get rid of parentheses
x∈R
-2x-1/3x-2-3=0
We multiply all the terms by the denominator
-2x*3x-2*3x-3*3x-1=0
Wy multiply elements
-6x^2-6x-9x-1=0
We add all the numbers together, and all the variables
-6x^2-15x-1=0
a = -6; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·(-6)·(-1)
Δ = 201
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{201}}{2*-6}=\frac{15-\sqrt{201}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*-6}=\frac{15+\sqrt{201}}{-12} $
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