7a+10/a=19

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

7a+10/a=19

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

7a^2-19a+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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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