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42x-126/7x+14=0
Domain of the equation: 7x!=0We multiply all the terms by the denominator
x!=0/7
x!=0
x∈R
42x*7x+14*7x-126=0
Wy multiply elements
294x^2+98x-126=0
a = 294; b = 98; c = -126;
Δ = b2-4ac
Δ = 982-4·294·(-126)
Δ = 157780
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{157780}=\sqrt{196*805}=\sqrt{196}*\sqrt{805}=14\sqrt{805}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-14\sqrt{805}}{2*294}=\frac{-98-14\sqrt{805}}{588} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+14\sqrt{805}}{2*294}=\frac{-98+14\sqrt{805}}{588} $
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