2/5(10x-2)=3x-1/5(25x-8)

Solution for 2/5(10x-2)=3x-1/5(25x-8) equation:

2/5(10x-2)=3x-1/5(25x-8)

We move all terms to the left:

2/5(10x-2)-(3x-1/5(25x-8))=0


Domain of the equation: 5(10x-2)!=0

x∈R



Domain of the equation: 5(25x-8))!=0

x∈R


We calculate fractions


(10x2/(5(10x-2)*5(25x-8)))+(-(3x-5x1)/(5(10x-2)*5(25x-8)))=0


We calculate terms in parentheses: +(10x2/(5(10x-2)*5(25x-8))), so:

10x2/(5(10x-2)*5(25x-8))

We multiply all the terms by the denominator


10x2

We add all the numbers together, and all the variables

10x^2

Back to the equation:

+(10x^2)



We calculate terms in parentheses: +(-(3x-5x1)/(5(10x-2)*5(25x-8))), so:

-(3x-5x1)/(5(10x-2)*5(25x-8))

We add all the numbers together, and all the variables

-(-2x)/(5(10x-2)*5(25x-8))

We multiply all the terms by the denominator


-(-2x)

We get rid of parentheses

2x

Back to the equation:

+(2x)


a = 10; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*10}=\frac{0}{20}
=0
$