1/5x+1/4=-10/3x-10

Solution for 1/5x+1/4=-10/3x-10 equation:

1/5x+1/4=-10/3x-10

We move all terms to the left:

1/5x+1/4-(-10/3x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

1/5x+10/3x+10+1/4=0

We calculate fractions


45x^2/240x^2+48x/240x^2+800x/240x^2+10=0

We multiply all the terms by the denominator


45x^2+48x+800x+10*240x^2=0

We add all the numbers together, and all the variables

45x^2+848x+10*240x^2=0

Wy multiply elements

45x^2+2400x^2+848x=0

We add all the numbers together, and all the variables

2445x^2+848x=0

a = 2445; b = 848; c = 0;
Δ = b2-4ac
Δ = 8482-4·2445·0
Δ = 719104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{719104}=848$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(848)-848}{2*2445}=\frac{-1696}{4890}
=-848/2445
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(848)+848}{2*2445}=\frac{0}{4890}
=0
$