2x+1/3=4(4/5x+5)

Solution for 2x+1/3=4(4/5x+5) equation:

2x+1/3=4(4/5x+5)

We move all terms to the left:

2x+1/3-(4(4/5x+5))=0


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

x∈R


We calculate fractions


2x+()/5x+5x/5x=0

Fractions to decimals

()/5x+2x+1=0

We multiply all the terms by the denominator


2x*5x+1*5x+()=0

We add all the numbers together, and all the variables

2x*5x+1*5x=0

Wy multiply elements

10x^2+5x=0

a = 10; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·10·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*10}=\frac{-10}{20}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*10}=\frac{0}{20}
=0
$