4/5x-8=6+1/4x

Solution for 4/5x-8=6+1/4x equation:

4/5x-8=6+1/4x

We move all terms to the left:

4/5x-8-(6+1/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(1/4x+6)-8=0

We get rid of parentheses

4/5x-1/4x-6-8=0

We calculate fractions


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

We add all the numbers together, and all the variables

16x/20x^2+(-5x)/20x^2-14=0

We multiply all the terms by the denominator


16x+(-5x)-14*20x^2=0

Wy multiply elements

-280x^2+16x+(-5x)=0

We get rid of parentheses

-280x^2+16x-5x=0

We add all the numbers together, and all the variables

-280x^2+11x=0

a = -280; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-280)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-280}=\frac{-22}{-560}
=11/280
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-280}=\frac{0}{-560}
=0
$