2/3x-20x=-6

Solution for 2/3x-20x=-6 equation:

2/3x-20x=-6

We move all terms to the left:

2/3x-20x-(-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-20x+2/3x+6=0

We multiply all the terms by the denominator


-20x*3x+6*3x+2=0

Wy multiply elements

-60x^2+18x+2=0

a = -60; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-60)·2
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{201}}{2*-60}=\frac{-18-2\sqrt{201}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{201}}{2*-60}=\frac{-18+2\sqrt{201}}{-120}
$