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1/3x=2x+14
We move all terms to the left:
1/3x-(2x+14)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
1/3x-2x-14=0
We multiply all the terms by the denominator
-2x*3x-14*3x+1=0
Wy multiply elements
-6x^2-42x+1=0
a = -6; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·(-6)·1
Δ = 1788
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{447}}{2*-6}=\frac{42-2\sqrt{447}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{447}}{2*-6}=\frac{42+2\sqrt{447}}{-12} $
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