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4x+2/3x=28
We move all terms to the left:
4x+2/3x-(28)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
4x*3x-28*3x+2=0
Wy multiply elements
12x^2-84x+2=0
a = 12; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·12·2
Δ = 6960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{435}}{2*12}=\frac{84-4\sqrt{435}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{435}}{2*12}=\frac{84+4\sqrt{435}}{24} $
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