7x+10/x=19

Solution for 7x+10/x=19 equation:

7x+10/x=19

We move all terms to the left:

7x+10/x-(19)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


7x*x-19*x+10=0

We add all the numbers together, and all the variables

-19x+7x*x+10=0

Wy multiply elements

7x^2-19x+10=0

a = 7; b = -19; c = +10;
Δ = b2-4ac
Δ = -192-4·7·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-9}{2*7}=\frac{10}{14}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+9}{2*7}=\frac{28}{14}
=2
$