-3/4+2/5x=7/20x-20

Solution for -3/4+2/5x=7/20x-20 equation:

-3/4+2/5x=7/20x-20

We move all terms to the left:

-3/4+2/5x-(7/20x-20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/5x-7/20x+20-3/4=0

We calculate fractions


(-600x^2)/1600x^2+640x/1600x^2+(-560x)/1600x^2+20=0

We multiply all the terms by the denominator


(-600x^2)+640x+(-560x)+20*1600x^2=0

Wy multiply elements

(-600x^2)+32000x^2+640x+(-560x)=0

We get rid of parentheses

-600x^2+32000x^2+640x-560x=0

We add all the numbers together, and all the variables

31400x^2+80x=0

a = 31400; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·31400·0
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*31400}=\frac{-160}{62800}
=-2/785
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*31400}=\frac{0}{62800}
=0
$