4x(7/x)+2/3=19x-2

Solution for 4x(7/x)+2/3=19x-2 equation:

4x(7/x)+2/3=19x-2

We move all terms to the left:

4x(7/x)+2/3-(19x-2)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x(+7/x)-(19x-2)+2/3=0

We multiply parentheses

28x^2-(19x-2)+2/3=0

We get rid of parentheses

28x^2-19x+2+2/3=0

We multiply all the terms by the denominator


28x^2*3-19x*3+2+2*3=0

We add all the numbers together, and all the variables

28x^2*3-19x*3+8=0

Wy multiply elements

84x^2-57x+8=0

a = 84; b = -57; c = +8;
Δ = b2-4ac
Δ = -572-4·84·8
Δ = 561
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{-(-57)-\sqrt{561}}{2*84}=\frac{57-\sqrt{561}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{561}}{2*84}=\frac{57+\sqrt{561}}{168}
$