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-1x-1=1/3x+3
We move all terms to the left:
-1x-1-(1/3x+3)=0
Domain of the equation: 3x+3)!=0We get rid of parentheses
x∈R
-1x-1/3x-3-1=0
We multiply all the terms by the denominator
-1x*3x-3*3x-1*3x-1=0
Wy multiply elements
-3x^2-9x-3x-1=0
We add all the numbers together, and all the variables
-3x^2-12x-1=0
a = -3; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-3)·(-1)
Δ = 132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*-3}=\frac{12-2\sqrt{33}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*-3}=\frac{12+2\sqrt{33}}{-6} $
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