-11,5+3/5x=4/20x+8,5

Solution for -11,5+3/5x=4/20x+8,5 equation:

-11.5+3/5x=4/20x+8.5

We move all terms to the left:

-11.5+3/5x-(4/20x+8.5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x+8.5)!=0

x∈R


We get rid of parentheses

3/5x-4/20x-8.5-11.5=0

We calculate fractions


60x/100x^2+(-20x)/100x^2-8.5-11.5=0

We add all the numbers together, and all the variables

60x/100x^2+(-20x)/100x^2-20=0

We multiply all the terms by the denominator


60x+(-20x)-20*100x^2=0

Wy multiply elements

-2000x^2+60x+(-20x)=0

We get rid of parentheses

-2000x^2+60x-20x=0

We add all the numbers together, and all the variables

-2000x^2+40x=0

a = -2000; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-2000)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-2000}=\frac{-80}{-4000}
=1/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-2000}=\frac{0}{-4000}
=0
$