1/2x+7/5=3+1/5x

Solution for 1/2x+7/5=3+1/5x equation:

1/2x+7/5=3+1/5x

We move all terms to the left:

1/2x+7/5-(3+1/5x)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x-(1/5x+3)+7/5=0

We get rid of parentheses

1/2x-1/5x-3+7/5=0

We calculate fractions


125x/250x^2+(-2x)/250x^2+14x/250x^2-3=0

We multiply all the terms by the denominator


125x+(-2x)+14x-3*250x^2=0

We add all the numbers together, and all the variables

139x+(-2x)-3*250x^2=0

Wy multiply elements

-750x^2+139x+(-2x)=0

We get rid of parentheses

-750x^2+139x-2x=0

We add all the numbers together, and all the variables

-750x^2+137x=0

a = -750; b = 137; c = 0;
Δ = b2-4ac
Δ = 1372-4·(-750)·0
Δ = 18769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18769}=137$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(137)-137}{2*-750}=\frac{-274}{-1500}
=137/750
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(137)+137}{2*-750}=\frac{0}{-1500}
=0
$