5/4x-6=5+5/8x

Solution for 5/4x-6=5+5/8x equation:

5/4x-6=5+5/8x

We move all terms to the left:

5/4x-6-(5+5/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(5/8x+5)-6=0

We get rid of parentheses

5/4x-5/8x-5-6=0

We calculate fractions


40x/32x^2+(-20x)/32x^2-5-6=0

We add all the numbers together, and all the variables

40x/32x^2+(-20x)/32x^2-11=0

We multiply all the terms by the denominator


40x+(-20x)-11*32x^2=0

Wy multiply elements

-352x^2+40x+(-20x)=0

We get rid of parentheses

-352x^2+40x-20x=0

We add all the numbers together, and all the variables

-352x^2+20x=0

a = -352; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-352)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-352}=\frac{-40}{-704}
=5/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-352}=\frac{0}{-704}
=0
$