5/4x+47=-9/5x-75

Solution for 5/4x+47=-9/5x-75 equation:

5/4x+47=-9/5x-75

We move all terms to the left:

5/4x+47-(-9/5x-75)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-75)!=0

x∈R


We get rid of parentheses

5/4x+9/5x+75+47=0

We calculate fractions


25x/20x^2+36x/20x^2+75+47=0

We add all the numbers together, and all the variables

25x/20x^2+36x/20x^2+122=0

We multiply all the terms by the denominator


25x+36x+122*20x^2=0

We add all the numbers together, and all the variables

61x+122*20x^2=0

Wy multiply elements

2440x^2+61x=0

a = 2440; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·2440·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*2440}=\frac{-122}{4880}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*2440}=\frac{0}{4880}
=0
$