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4x+7/2x=14
We move all terms to the left:
4x+7/2x-(14)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
4x*2x-14*2x+7=0
Wy multiply elements
8x^2-28x+7=0
a = 8; b = -28; c = +7;
Δ = b2-4ac
Δ = -282-4·8·7
Δ = 560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{35}}{2*8}=\frac{28-4\sqrt{35}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{35}}{2*8}=\frac{28+4\sqrt{35}}{16} $
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