1/5x+3=1/4x-7

Solution for 1/5x+3=1/4x-7 equation:

1/5x+3=1/4x-7

We move all terms to the left:

1/5x+3-(1/4x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

1/5x-1/4x+7+3=0

We calculate fractions


4x/20x^2+(-5x)/20x^2+7+3=0

We add all the numbers together, and all the variables

4x/20x^2+(-5x)/20x^2+10=0

We multiply all the terms by the denominator


4x+(-5x)+10*20x^2=0

Wy multiply elements

200x^2+4x+(-5x)=0

We get rid of parentheses

200x^2+4x-5x=0

We add all the numbers together, and all the variables

200x^2-1x=0

a = 200; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·200·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*200}=\frac{0}{400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*200}=\frac{2}{400}
=1/200
$