7x-3=19/5x

Solution for 7x-3=19/5x equation:

7x-3=19/5x

We move all terms to the left:

7x-3-(19/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+19/5x)-3=0

We get rid of parentheses

7x-19/5x-3=0

We multiply all the terms by the denominator


7x*5x-3*5x-19=0

Wy multiply elements

35x^2-15x-19=0

a = 35; b = -15; c = -19;
Δ = b2-4ac
Δ = -152-4·35·(-19)
Δ = 2885
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{-(-15)-\sqrt{2885}}{2*35}=\frac{15-\sqrt{2885}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{2885}}{2*35}=\frac{15+\sqrt{2885}}{70}
$