34-5/2x=2/5x+5

Solution for 34-5/2x=2/5x+5 equation:

34-5/2x=2/5x+5

We move all terms to the left:

34-5/2x-(2/5x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

-5/2x-2/5x-5+34=0

We calculate fractions


(-25x)/10x^2+(-4x)/10x^2-5+34=0

We add all the numbers together, and all the variables

(-25x)/10x^2+(-4x)/10x^2+29=0

We multiply all the terms by the denominator


(-25x)+(-4x)+29*10x^2=0

Wy multiply elements

290x^2+(-25x)+(-4x)=0

We get rid of parentheses

290x^2-25x-4x=0

We add all the numbers together, and all the variables

290x^2-29x=0

a = 290; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·290·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*290}=\frac{0}{580}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*290}=\frac{58}{580}
=1/10
$