2x+7)/9=4x-1)/5

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Solution for 2x+7)/9=4x-1)/5 equation:



2x+7)/9=4x-1)/5
We move all terms to the left:
2x+7)/9-(4x-1)/5)=0
Domain of the equation: 9-(4x!=0
We move all terms containing x to the left, all other terms to the right
-(4x!=-9
x∈R
We calculate fractions
2x+()/(-20x+9)-4x/(-20x+9)+(-1)*9=0
We add all the numbers together, and all the variables
2x+()/(-20x+9)-4x/(-20x+9)-9=0
We multiply all the terms by the denominator
2x*(-20x+9)-4x-9*(-20x+9)+()=0
We add all the numbers together, and all the variables
-4x+2x*(-20x+9)-9*(-20x+9)=0
We multiply parentheses
-40x^2-4x+18x+180x-81=0
We add all the numbers together, and all the variables
-40x^2+194x-81=0
a = -40; b = 194; c = -81;
Δ = b2-4ac
Δ = 1942-4·(-40)·(-81)
Δ = 24676
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:
$\sqrt{\Delta}=\sqrt{24676}=\sqrt{4*6169}=\sqrt{4}*\sqrt{6169}=2\sqrt{6169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(194)-2\sqrt{6169}}{2*-40}=\frac{-194-2\sqrt{6169}}{-80} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(194)+2\sqrt{6169}}{2*-40}=\frac{-194+2\sqrt{6169}}{-80} $

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