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4x-7/3x=14
We move all terms to the left:
4x-7/3x-(14)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
4x*3x-14*3x-7=0
Wy multiply elements
12x^2-42x-7=0
a = 12; b = -42; c = -7;
Δ = b2-4ac
Δ = -422-4·12·(-7)
Δ = 2100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-10\sqrt{21}}{2*12}=\frac{42-10\sqrt{21}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+10\sqrt{21}}{2*12}=\frac{42+10\sqrt{21}}{24} $
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