4/5-5/8x=7/20x-1

Solution for 4/5-5/8x=7/20x-1 equation:

4/5-5/8x=7/20x-1

We move all terms to the left:

4/5-5/8x-(7/20x-1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 20x-1)!=0

x∈R


We get rid of parentheses

-5/8x-7/20x+1+4/5=0

We calculate fractions


1280x^2/4000x^2+(-2500x)/4000x^2+(-1400x)/4000x^2+1=0

We multiply all the terms by the denominator


1280x^2+(-2500x)+(-1400x)+1*4000x^2=0

Wy multiply elements

1280x^2+4000x^2+(-2500x)+(-1400x)=0

We get rid of parentheses

1280x^2+4000x^2-2500x-1400x=0

We add all the numbers together, and all the variables

5280x^2-3900x=0

a = 5280; b = -3900; c = 0;
Δ = b2-4ac
Δ = -39002-4·5280·0
Δ = 15210000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15210000}=3900$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3900)-3900}{2*5280}=\frac{0}{10560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3900)+3900}{2*5280}=\frac{7800}{10560}
=65/88
$