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2x+3/4x=99
We move all terms to the left:
2x+3/4x-(99)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
2x*4x-99*4x+3=0
Wy multiply elements
8x^2-396x+3=0
a = 8; b = -396; c = +3;
Δ = b2-4ac
Δ = -3962-4·8·3
Δ = 156720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{156720}=\sqrt{16*9795}=\sqrt{16}*\sqrt{9795}=4\sqrt{9795}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9795}}{2*8}=\frac{396-4\sqrt{9795}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9795}}{2*8}=\frac{396+4\sqrt{9795}}{16} $
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