5/4x-3/5=2-7/2x

Solution for 5/4x-3/5=2-7/2x equation:

5/4x-3/5=2-7/2x

We move all terms to the left:

5/4x-3/5-(2-7/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(-7/2x+2)-3/5=0

We get rid of parentheses

5/4x+7/2x-2-3/5=0

We calculate fractions


(-48x^2)/200x^2+250x/200x^2+700x/200x^2-2=0

We multiply all the terms by the denominator


(-48x^2)+250x+700x-2*200x^2=0

We add all the numbers together, and all the variables

(-48x^2)+950x-2*200x^2=0

Wy multiply elements

(-48x^2)-400x^2+950x=0

We get rid of parentheses

-48x^2-400x^2+950x=0

We add all the numbers together, and all the variables

-448x^2+950x=0

a = -448; b = 950; c = 0;
Δ = b2-4ac
Δ = 9502-4·(-448)·0
Δ = 902500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{902500}=950$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(950)-950}{2*-448}=\frac{-1900}{-896}
=2+27/224
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(950)+950}{2*-448}=\frac{0}{-896}
=0
$