19+x=2/7x+4

Solution for 19+x=2/7x+4 equation:

19+x=2/7x+4

We move all terms to the left:

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


Domain of the equation: 7x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

7x^2-28x+133x-2=0

We add all the numbers together, and all the variables

7x^2+105x-2=0

a = 7; b = 105; c = -2;
Δ = b2-4ac
Δ = 1052-4·7·(-2)
Δ = 11081
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{-(105)-\sqrt{11081}}{2*7}=\frac{-105-\sqrt{11081}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11081}}{2*7}=\frac{-105+\sqrt{11081}}{14}
$