19-7x=5/3x+6

Solution for 19-7x=5/3x+6 equation:

19-7x=5/3x+6

We move all terms to the left:

19-7x-(5/3x+6)=0


Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

-7x-5/3x-6+19=0

We multiply all the terms by the denominator


-7x*3x-6*3x+19*3x-5=0

Wy multiply elements

-21x^2-18x+57x-5=0

We add all the numbers together, and all the variables

-21x^2+39x-5=0

a = -21; b = 39; c = -5;
Δ = b2-4ac
Δ = 392-4·(-21)·(-5)
Δ = 1101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-\sqrt{1101}}{2*-21}=\frac{-39-\sqrt{1101}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1101}}{2*-21}=\frac{-39+\sqrt{1101}}{-42}
$