6x-1=2/3x+19

Solution for 6x-1=2/3x+19 equation:

6x-1=2/3x+19

We move all terms to the left:

6x-1-(2/3x+19)=0


Domain of the equation: 3x+19)!=0

x∈R


We get rid of parentheses

6x-2/3x-19-1=0

We multiply all the terms by the denominator


6x*3x-19*3x-1*3x-2=0

Wy multiply elements

18x^2-57x-3x-2=0

We add all the numbers together, and all the variables

18x^2-60x-2=0

a = 18; b = -60; c = -2;
Δ = b2-4ac
Δ = -602-4·18·(-2)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{26}}{2*18}=\frac{60-12\sqrt{26}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{26}}{2*18}=\frac{60+12\sqrt{26}}{36}
$