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x+1=1/3x-7
We move all terms to the left:
x+1-(1/3x-7)=0
Domain of the equation: 3x-7)!=0We get rid of parentheses
x∈R
x-1/3x+7+1=0
We multiply all the terms by the denominator
x*3x+7*3x+1*3x-1=0
Wy multiply elements
3x^2+21x+3x-1=0
We add all the numbers together, and all the variables
3x^2+24x-1=0
a = 3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·3·(-1)
Δ = 588
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-14\sqrt{3}}{2*3}=\frac{-24-14\sqrt{3}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+14\sqrt{3}}{2*3}=\frac{-24+14\sqrt{3}}{6} $
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