2/3x+4=5x-20

Solution for 2/3x+4=5x-20 equation:

2/3x+4=5x-20

We move all terms to the left:

2/3x+4-(5x-20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-5x+20+4=0

We multiply all the terms by the denominator


-5x*3x+20*3x+4*3x+2=0

Wy multiply elements

-15x^2+60x+12x+2=0

We add all the numbers together, and all the variables

-15x^2+72x+2=0

a = -15; b = 72; c = +2;
Δ = b2-4ac
Δ = 722-4·(-15)·2
Δ = 5304
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:

$\sqrt{\Delta}=\sqrt{5304}=\sqrt{4*1326}=\sqrt{4}*\sqrt{1326}=2\sqrt{1326}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1326}}{2*-15}=\frac{-72-2\sqrt{1326}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1326}}{2*-15}=\frac{-72+2\sqrt{1326}}{-30}
$