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

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



(5/4x+1)=7/5x-2
We move all terms to the left:
(5/4x+1)-(7/5x-2)=0
Domain of the equation: 4x+1)!=0
x∈R
Domain of the equation: 5x-2)!=0
x∈R
We get rid of parentheses
5/4x-7/5x+1+2=0
We calculate fractions
25x/20x^2+(-28x)/20x^2+1+2=0
We add all the numbers together, and all the variables
25x/20x^2+(-28x)/20x^2+3=0
We multiply all the terms by the denominator
25x+(-28x)+3*20x^2=0
Wy multiply elements
60x^2+25x+(-28x)=0
We get rid of parentheses
60x^2+25x-28x=0
We add all the numbers together, and all the variables
60x^2-3x=0
a = 60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·60·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*60}=\frac{0}{120} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*60}=\frac{6}{120} =1/20 $

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