-5/4x+4=7/5x-1

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

-5/4x+4=7/5x-1

We move all terms to the left:

-5/4x+4-(7/5x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

-5/4x-7/5x+1+4=0

We calculate fractions


(-25x)/20x^2+(-28x)/20x^2+1+4=0

We add all the numbers together, and all the variables

(-25x)/20x^2+(-28x)/20x^2+5=0

We multiply all the terms by the denominator


(-25x)+(-28x)+5*20x^2=0

Wy multiply elements

100x^2+(-25x)+(-28x)=0

We get rid of parentheses

100x^2-25x-28x=0

We add all the numbers together, and all the variables

100x^2-53x=0

a = 100; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·100·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*100}=\frac{0}{200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*100}=\frac{106}{200}
=53/100
$