1/4x+7=20-1/12x

Solution for 1/4x+7=20-1/12x equation:

1/4x+7=20-1/12x

We move all terms to the left:

1/4x+7-(20-1/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-1/12x+20)+7=0

We get rid of parentheses

1/4x+1/12x-20+7=0

We calculate fractions


12x/48x^2+4x/48x^2-20+7=0

We add all the numbers together, and all the variables

12x/48x^2+4x/48x^2-13=0

We multiply all the terms by the denominator


12x+4x-13*48x^2=0

We add all the numbers together, and all the variables

16x-13*48x^2=0

Wy multiply elements

-624x^2+16x=0

a = -624; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-624)·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*-624}=\frac{-32}{-1248}
=1/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-624}=\frac{0}{-1248}
=0
$