1/4x+1/3=-10/3x-25

Solution for 1/4x+1/3=-10/3x-25 equation:

1/4x+1/3=-10/3x-25

We move all terms to the left:

1/4x+1/3-(-10/3x-25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-25)!=0

x∈R


We get rid of parentheses

1/4x+10/3x+25+1/3=0

We calculate fractions


27x/108x^2+40x/108x^2+4x/108x^2+25=0

We multiply all the terms by the denominator


27x+40x+4x+25*108x^2=0

We add all the numbers together, and all the variables

71x+25*108x^2=0

Wy multiply elements

2700x^2+71x=0

a = 2700; b = 71; c = 0;
Δ = b2-4ac
Δ = 712-4·2700·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-71}{2*2700}=\frac{-142}{5400}
=-71/2700
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+71}{2*2700}=\frac{0}{5400}
=0
$