1/5x-31/10=7/4x

Solution for 1/5x-31/10=7/4x equation:

1/5x-31/10=7/4x

We move all terms to the left:

1/5x-31/10-(7/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(+7/4x)-31/10=0

We get rid of parentheses

1/5x-7/4x-31/10=0

We calculate fractions


(-2480x^2)/200x^2+40x/200x^2+(-350x)/200x^2=0

We multiply all the terms by the denominator


(-2480x^2)+40x+(-350x)=0

We get rid of parentheses

-2480x^2+40x-350x=0

We add all the numbers together, and all the variables

-2480x^2-310x=0

a = -2480; b = -310; c = 0;
Δ = b2-4ac
Δ = -3102-4·(-2480)·0
Δ = 96100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{96100}=310$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-310)-310}{2*-2480}=\frac{0}{-4960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-310)+310}{2*-2480}=\frac{620}{-4960}
=-1/8
$