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1/3x+11=2x-7
We move all terms to the left:
1/3x+11-(2x-7)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
1/3x-2x+7+11=0
We multiply all the terms by the denominator
-2x*3x+7*3x+11*3x+1=0
Wy multiply elements
-6x^2+21x+33x+1=0
We add all the numbers together, and all the variables
-6x^2+54x+1=0
a = -6; b = 54; c = +1;
Δ = b2-4ac
Δ = 542-4·(-6)·1
Δ = 2940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-14\sqrt{15}}{2*-6}=\frac{-54-14\sqrt{15}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+14\sqrt{15}}{2*-6}=\frac{-54+14\sqrt{15}}{-12} $
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