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4/3x=14-x
We move all terms to the left:
4/3x-(14-x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
4/3x-(-1x+14)=0
We get rid of parentheses
4/3x+1x-14=0
We multiply all the terms by the denominator
1x*3x-14*3x+4=0
Wy multiply elements
3x^2-42x+4=0
a = 3; b = -42; c = +4;
Δ = b2-4ac
Δ = -422-4·3·4
Δ = 1716
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{429}}{2*3}=\frac{42-2\sqrt{429}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{429}}{2*3}=\frac{42+2\sqrt{429}}{6} $
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