X(3-1/x)+x=4(1-4)+10

Solution for X(3-1/x)+x=4(1-4)+10 equation:

X(3-1/X)+X=4(1-4)+10

We move all terms to the left:

X(3-1/X)+X-(4(1-4)+10)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X(-1/X+3)+X-(4(-3)+10)=0

We add all the numbers together, and all the variables

X+X(-1/X+3)+2=0

We multiply parentheses

-1X^2+X+3X+2=0

We add all the numbers together, and all the variables

-1X^2+4X+2=0

a = -1; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-1)·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*-1}=\frac{-4-2\sqrt{6}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*-1}=\frac{-4+2\sqrt{6}}{-2}
$