2/7x=3x+19

Solution for 2/7x=3x+19 equation:

2/7x=3x+19

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

2/7x-3x-19=0

We multiply all the terms by the denominator


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

Wy multiply elements

-21x^2-133x+2=0

a = -21; b = -133; c = +2;
Δ = b2-4ac
Δ = -1332-4·(-21)·2
Δ = 17857
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{-(-133)-\sqrt{17857}}{2*-21}=\frac{133-\sqrt{17857}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+\sqrt{17857}}{2*-21}=\frac{133+\sqrt{17857}}{-42}
$