5(1/5x+3)=5(3/10x+4)

Solution for 5(1/5x+3)=5(3/10x+4) equation:

5(1/5x+3)=5(3/10x+4)

We move all terms to the left:

5(1/5x+3)-(5(3/10x+4))=0


Domain of the equation: 5x+3)!=0

x∈R



Domain of the equation: 10x+4))!=0

x∈R


We multiply parentheses

5x-(5(3/10x+4))+15=0

We multiply all the terms by the denominator


5x*10x+15*10x+4))-(5(3+4))=0

We add all the numbers together, and all the variables

5x*10x+15*10x+4))-(57)=0

We add all the numbers together, and all the variables

5x*10x+15*10x=0

Wy multiply elements

50x^2+150x=0

a = 50; b = 150; c = 0;
Δ = b2-4ac
Δ = 1502-4·50·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-150}{2*50}=\frac{-300}{100}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+150}{2*50}=\frac{0}{100}
=0
$