5x/5(2-3x)=1/25

Solution for 5x/5(2-3x)=1/25 equation:

5x/5(2-3x)=1/25

We move all terms to the left:

5x/5(2-3x)-(1/25)=0


Domain of the equation: 5(2-3x)!=0

x∈R


We add all the numbers together, and all the variables

5x/5(-3x+2)-(+1/25)=0

We get rid of parentheses

5x/5(-3x+2)-1/25=0

We calculate fractions


125x/(-375x+250)+(-5x(-)/(-375x+250)=0


We calculate terms in parentheses: +(-5x(-)/(-375x+250), so:

-5x(-)/(-375x+250

We add all the numbers together, and all the variables

-5x0/(-375x+250

We multiply all the terms by the denominator


-5x0

We add all the numbers together, and all the variables

-5x

Back to the equation:

+(-5x)


We get rid of parentheses

125x/(-375x+250)-5x=0

We multiply all the terms by the denominator


125x-5x*(-375x+250)=0

We multiply parentheses

1875x^2+125x-1250x=0

We add all the numbers together, and all the variables

1875x^2-1125x=0

a = 1875; b = -1125; c = 0;
Δ = b2-4ac
Δ = -11252-4·1875·0
Δ = 1265625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1265625}=1125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1125)-1125}{2*1875}=\frac{0}{3750}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1125)+1125}{2*1875}=\frac{2250}{3750}
=3/5
$