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

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
$