5/4x+6-7/4x=8+4/5x

Solution for 5/4x+6-7/4x=8+4/5x equation:

5/4x+6-7/4x=8+4/5x

We move all terms to the left:

5/4x+6-7/4x-(8+4/5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-7/4x-(4/5x+8)+6=0

We get rid of parentheses

5/4x-7/4x-4/5x-8+6=0

We calculate fractions


(-35x+5)/20x^2+(-16x)/20x^2-8+6=0

We add all the numbers together, and all the variables

(-35x+5)/20x^2+(-16x)/20x^2-2=0

We multiply all the terms by the denominator


(-35x+5)+(-16x)-2*20x^2=0

Wy multiply elements

-40x^2+(-35x+5)+(-16x)=0

We get rid of parentheses

-40x^2-35x-16x+5=0

We add all the numbers together, and all the variables

-40x^2-51x+5=0

a = -40; b = -51; c = +5;
Δ = b2-4ac
Δ = -512-4·(-40)·5
Δ = 3401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{3401}}{2*-40}=\frac{51-\sqrt{3401}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{3401}}{2*-40}=\frac{51+\sqrt{3401}}{-80}
$