10(3/5x+4)=20(3/10x+7)

Solution for 10(3/5x+4)=20(3/10x+7) equation:

10(3/5x+4)=20(3/10x+7)

We move all terms to the left:

10(3/5x+4)-(20(3/10x+7))=0


Domain of the equation: 5x+4)!=0

x∈R



Domain of the equation: 10x+7))!=0

x∈R


We multiply parentheses

30x-(20(3/10x+7))+40=0

We multiply all the terms by the denominator


30x*10x+40*10x+7))-(20(3+7))=0

We add all the numbers together, and all the variables

30x*10x+40*10x+7))-(2010)=0

We add all the numbers together, and all the variables

30x*10x+40*10x=0

Wy multiply elements

300x^2+400x=0

a = 300; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·300·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*300}=\frac{-800}{600}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*300}=\frac{0}{600}
=0
$