2x+5/7x=19

Solution for 2x+5/7x=19 equation:

2x+5/7x=19

We move all terms to the left:

2x+5/7x-(19)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


2x*7x-19*7x+5=0

Wy multiply elements

14x^2-133x+5=0

a = 14; b = -133; c = +5;
Δ = b2-4ac
Δ = -1332-4·14·5
Δ = 17409
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{17409}}{2*14}=\frac{133-\sqrt{17409}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+\sqrt{17409}}{2*14}=\frac{133+\sqrt{17409}}{28}
$