2/5(10x+15)=3/10(20x+30)

Solution for 2/5(10x+15)=3/10(20x+30) equation:

2/5(10x+15)=3/10(20x+30)

We move all terms to the left:

2/5(10x+15)-(3/10(20x+30))=0


Domain of the equation: 5(10x+15)!=0

x∈R



Domain of the equation: 10(20x+30))!=0

x∈R


We calculate fractions


(20x2/(5(10x+15)*10(20x+30)))+(-15x1/(5(10x+15)*10(20x+30)))=0


We calculate terms in parentheses: +(20x2/(5(10x+15)*10(20x+30))), so:

20x2/(5(10x+15)*10(20x+30))

We multiply all the terms by the denominator


20x2

We add all the numbers together, and all the variables

20x^2

Back to the equation:

+(20x^2)



We calculate terms in parentheses: +(-15x1/(5(10x+15)*10(20x+30))), so:

-15x1/(5(10x+15)*10(20x+30))

We multiply all the terms by the denominator


-15x1

We add all the numbers together, and all the variables

-15x

Back to the equation:

+(-15x)


We get rid of parentheses

20x^2-15x=0

a = 20; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·20·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*20}=\frac{30}{40}
=3/4
$