1/5x+1/4=10/3x-12

Solution for 1/5x+1/4=10/3x-12 equation:

1/5x+1/4=10/3x-12

We move all terms to the left:

1/5x+1/4-(10/3x-12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-12)!=0

x∈R


We get rid of parentheses

1/5x-10/3x+12+1/4=0

We calculate fractions


45x^2/240x^2+48x/240x^2+(-800x)/240x^2+12=0

We multiply all the terms by the denominator


45x^2+48x+(-800x)+12*240x^2=0

Wy multiply elements

45x^2+2880x^2+48x+(-800x)=0

We get rid of parentheses

45x^2+2880x^2+48x-800x=0

We add all the numbers together, and all the variables

2925x^2-752x=0

a = 2925; b = -752; c = 0;
Δ = b2-4ac
Δ = -7522-4·2925·0
Δ = 565504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{565504}=752$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-752)-752}{2*2925}=\frac{0}{5850}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-752)+752}{2*2925}=\frac{1504}{5850}
=752/2925
$