1/5x-1=-11/20x-8

Solution for 1/5x-1=-11/20x-8 equation:

1/5x-1=-11/20x-8

We move all terms to the left:

1/5x-1-(-11/20x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x-8)!=0

x∈R


We get rid of parentheses

1/5x+11/20x+8-1=0

We calculate fractions


20x/100x^2+55x/100x^2+8-1=0

We add all the numbers together, and all the variables

20x/100x^2+55x/100x^2+7=0

We multiply all the terms by the denominator


20x+55x+7*100x^2=0

We add all the numbers together, and all the variables

75x+7*100x^2=0

Wy multiply elements

700x^2+75x=0

a = 700; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·700·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*700}=\frac{-150}{1400}
=-3/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*700}=\frac{0}{1400}
=0
$