4/20x+4=-3/5x+8

Solution for 4/20x+4=-3/5x+8 equation:

4/20x+4=-3/5x+8

We move all terms to the left:

4/20x+4-(-3/5x+8)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R



Domain of the equation: 5x+8)!=0

x∈R


We get rid of parentheses

4/20x+3/5x-8+4=0

We calculate fractions


20x/100x^2+60x/100x^2-8+4=0

We add all the numbers together, and all the variables

20x/100x^2+60x/100x^2-4=0

We multiply all the terms by the denominator


20x+60x-4*100x^2=0

We add all the numbers together, and all the variables

80x-4*100x^2=0

Wy multiply elements

-400x^2+80x=0

a = -400; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-400)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-400}=\frac{-160}{-800}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-400}=\frac{0}{-800}
=0
$