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7x-4/3x=4
We move all terms to the left:
7x-4/3x-(4)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
7x*3x-4*3x-4=0
Wy multiply elements
21x^2-12x-4=0
a = 21; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·21·(-4)
Δ = 480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{30}}{2*21}=\frac{12-4\sqrt{30}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{30}}{2*21}=\frac{12+4\sqrt{30}}{42} $
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