2/3x-7=4x-19

Solution for 2/3x-7=4x-19 equation:

2/3x-7=4x-19

We move all terms to the left:

2/3x-7-(4x-19)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x+19-7=0

We multiply all the terms by the denominator


-4x*3x+19*3x-7*3x+2=0

Wy multiply elements

-12x^2+57x-21x+2=0

We add all the numbers together, and all the variables

-12x^2+36x+2=0

a = -12; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·(-12)·2
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{87}}{2*-12}=\frac{-36-4\sqrt{87}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{87}}{2*-12}=\frac{-36+4\sqrt{87}}{-24}
$