98=4(1+2x)/(7X+1.09)x=

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Solution for 98=4(1+2x)/(7X+1.09)x= equation:



98=4(1+2x)/(7x+1.09)x=
We move all terms to the left:
98-(4(1+2x)/(7x+1.09)x)=0
Domain of the equation: (7x+1.09)x)!=0
x∈R
We add all the numbers together, and all the variables
-(4(2x+1)/(7x+1.09)x)+98=0
We multiply all the terms by the denominator
-(4(2x+1)+98*(7x+1.09)x)=0
We calculate terms in parentheses: -(4(2x+1)+98*(7x+1.09)x), so:
4(2x+1)+98*(7x+1.09)x
We multiply parentheses
686x^2+8x+106.82x+4
We add all the numbers together, and all the variables
686x^2+114.82x+4
Back to the equation:
-(686x^2+114.82x+4)
We get rid of parentheses
-686x^2-114.82x-4=0
a = -686; b = -114.82; c = -4;
Δ = b2-4ac
Δ = -114.822-4·(-686)·(-4)
Δ = 2207.6324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114.82)-\sqrt{2207.6324}}{2*-686}=\frac{114.82-\sqrt{2207.6324}}{-1372} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114.82)+\sqrt{2207.6324}}{2*-686}=\frac{114.82+\sqrt{2207.6324}}{-1372} $

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