2/3x+6-10x=30

Solution for 2/3x+6-10x=30 equation:

2/3x+6-10x=30

We move all terms to the left:

2/3x+6-10x-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+2/3x-24=0

We multiply all the terms by the denominator


-10x*3x-24*3x+2=0

Wy multiply elements

-30x^2-72x+2=0

a = -30; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·(-30)·2
Δ = 5424
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:

$\sqrt{\Delta}=\sqrt{5424}=\sqrt{16*339}=\sqrt{16}*\sqrt{339}=4\sqrt{339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{339}}{2*-30}=\frac{72-4\sqrt{339}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{339}}{2*-30}=\frac{72+4\sqrt{339}}{-60}
$