-4x+20=1/3x+4

Solution for -4x+20=1/3x+4 equation:

-4x+20=1/3x+4

We move all terms to the left:

-4x+20-(1/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

-4x-1/3x-4+20=0

We multiply all the terms by the denominator


-4x*3x-4*3x+20*3x-1=0

Wy multiply elements

-12x^2-12x+60x-1=0

We add all the numbers together, and all the variables

-12x^2+48x-1=0

a = -12; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·(-12)·(-1)
Δ = 2256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{141}}{2*-12}=\frac{-48-4\sqrt{141}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{141}}{2*-12}=\frac{-48+4\sqrt{141}}{-24}
$