(3/x)+3=4x-3

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

(3/x)+3=4x-3

We move all terms to the left:

(3/x)+3-(4x-3)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/x)-(4x-3)+3=0

We get rid of parentheses

3/x-4x+3+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-4x*x+3=0

Wy multiply elements

-4x^2+6x+3=0

a = -4; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-4)·3
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-4}=\frac{-6-2\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-4}=\frac{-6+2\sqrt{21}}{-8}
$