1/5x-1/4=1/6x-12

Solution for 1/5x-1/4=1/6x-12 equation:

1/5x-1/4=1/6x-12

We move all terms to the left:

1/5x-1/4-(1/6x-12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x-12)!=0

x∈R


We get rid of parentheses

1/5x-1/6x+12-1/4=0

We calculate fractions


(-180x^2)/480x^2+96x/480x^2+(-80x)/480x^2+12=0

We multiply all the terms by the denominator


(-180x^2)+96x+(-80x)+12*480x^2=0

Wy multiply elements

(-180x^2)+5760x^2+96x+(-80x)=0

We get rid of parentheses

-180x^2+5760x^2+96x-80x=0

We add all the numbers together, and all the variables

5580x^2+16x=0

a = 5580; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·5580·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*5580}=\frac{-32}{11160}
=-4/1395
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*5580}=\frac{0}{11160}
=0
$