4^2=x+12/x-3

Solution for 4^2=x+12/x-3 equation:

4^2=x+12/x-3

We move all terms to the left:

4^2-(x+12/x-3)=0


Domain of the equation: x-3)!=0

x∈R


We add all the numbers together, and all the variables

-(x+12/x-3)+16=0

We get rid of parentheses

-x-12/x+3+16=0

We multiply all the terms by the denominator


-x*x+3*x+16*x-12=0

We add all the numbers together, and all the variables

19x-x*x-12=0

Wy multiply elements

-1x^2+19x-12=0

a = -1; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·(-1)·(-12)
Δ = 313
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{-(19)-\sqrt{313}}{2*-1}=\frac{-19-\sqrt{313}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{313}}{2*-1}=\frac{-19+\sqrt{313}}{-2}
$