31/2x-21/5x=26

Solution for 31/2x-21/5x=26 equation:

31/2x-21/5x=26

We move all terms to the left:

31/2x-21/5x-(26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


155x/10x^2+(-42x)/10x^2-26=0

We multiply all the terms by the denominator


155x+(-42x)-26*10x^2=0

Wy multiply elements

-260x^2+155x+(-42x)=0

We get rid of parentheses

-260x^2+155x-42x=0

We add all the numbers together, and all the variables

-260x^2+113x=0

a = -260; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·(-260)·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*-260}=\frac{-226}{-520}
=113/260
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*-260}=\frac{0}{-520}
=0
$