6x-3/x+4=0

Solution for 6x-3/x+4=0 equation:

6x-3/x+4=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x+4*x-3=0

We add all the numbers together, and all the variables

4x+6x*x-3=0

Wy multiply elements

6x^2+4x-3=0

a = 6; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·6·(-3)
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{22}}{2*6}=\frac{-4-2\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{22}}{2*6}=\frac{-4+2\sqrt{22}}{12}
$