2x-3/3x=-28

Solution for 2x-3/3x=-28 equation:

2x-3/3x=-28

We move all terms to the left:

2x-3/3x-(-28)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x-3/3x+28=0

We multiply all the terms by the denominator


2x*3x+28*3x-3=0

Wy multiply elements

6x^2+84x-3=0

a = 6; b = 84; c = -3;
Δ = b2-4ac
Δ = 842-4·6·(-3)
Δ = 7128
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:

$\sqrt{\Delta}=\sqrt{7128}=\sqrt{324*22}=\sqrt{324}*\sqrt{22}=18\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-18\sqrt{22}}{2*6}=\frac{-84-18\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+18\sqrt{22}}{2*6}=\frac{-84+18\sqrt{22}}{12}
$