4/5x-8=18/20x+5

Solution for 4/5x-8=18/20x+5 equation:

4/5x-8=18/20x+5

We move all terms to the left:

4/5x-8-(18/20x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x+5)!=0

x∈R


We get rid of parentheses

4/5x-18/20x-5-8=0

We calculate fractions


80x/100x^2+(-90x)/100x^2-5-8=0

We add all the numbers together, and all the variables

80x/100x^2+(-90x)/100x^2-13=0

We multiply all the terms by the denominator


80x+(-90x)-13*100x^2=0

Wy multiply elements

-1300x^2+80x+(-90x)=0

We get rid of parentheses

-1300x^2+80x-90x=0

We add all the numbers together, and all the variables

-1300x^2-10x=0

a = -1300; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1300)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1300}=\frac{0}{-2600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1300}=\frac{20}{-2600}
=-1/130
$