1/4x+1/10=-3/20x-710

Solution for 1/4x+1/10=-3/20x-710 equation:

1/4x+1/10=-3/20x-710

We move all terms to the left:

1/4x+1/10-(-3/20x-710)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 20x-710)!=0

x∈R


We get rid of parentheses

1/4x+3/20x+710+1/10=0

We calculate fractions


160x^2/800x^2+200x/800x^2+120x/800x^2+710=0

We multiply all the terms by the denominator


160x^2+200x+120x+710*800x^2=0

We add all the numbers together, and all the variables

160x^2+320x+710*800x^2=0

Wy multiply elements

160x^2+568000x^2+320x=0

We add all the numbers together, and all the variables

568160x^2+320x=0

a = 568160; b = 320; c = 0;
Δ = b2-4ac
Δ = 3202-4·568160·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-320}{2*568160}=\frac{-640}{1136320}
=-2/3551
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+320}{2*568160}=\frac{0}{1136320}
=0
$