3/4x+5=2/5x

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

3/4x+5=2/5x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4x-2/5x+5=0

We calculate fractions


15x/20x^2+(-8x)/20x^2+5=0

We multiply all the terms by the denominator


15x+(-8x)+5*20x^2=0

Wy multiply elements

100x^2+15x+(-8x)=0

We get rid of parentheses

100x^2+15x-8x=0

We add all the numbers together, and all the variables

100x^2+7x=0

a = 100; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·100·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*100}=\frac{-14}{200}
=-7/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*100}=\frac{0}{200}
=0
$