2/5x-9/29x=2

Solution for 2/5x-9/29x=2 equation:

2/5x-9/29x=2

We move all terms to the left:

2/5x-9/29x-(2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 29x!=0

x!=0/29

x!=0

x∈R


We calculate fractions


58x/145x^2+(-45x)/145x^2-2=0

We multiply all the terms by the denominator


58x+(-45x)-2*145x^2=0

Wy multiply elements

-290x^2+58x+(-45x)=0

We get rid of parentheses

-290x^2+58x-45x=0

We add all the numbers together, and all the variables

-290x^2+13x=0

a = -290; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-290)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-290}=\frac{-26}{-580}
=13/290
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-290}=\frac{0}{-580}
=0
$