(2x+2)=10.5/x

Solution for (2x+2)=10.5/x equation:

(2x+2)=10.5/x

We move all terms to the left:

(2x+2)-(10.5/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(2x+2)-(+10.5/x)=0

We get rid of parentheses

2x-10.5/x+2=0

We multiply all the terms by the denominator


2x*x+2*x-10.5=0

We add all the numbers together, and all the variables

2x+2x*x-10.5=0

Wy multiply elements

2x^2+2x-10.5=0

a = 2; b = 2; c = -10.5;
Δ = b2-4ac
Δ = 22-4·2·(-10.5)
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{-(2)-2\sqrt{22}}{2*2}=\frac{-2-2\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*2}=\frac{-2+2\sqrt{22}}{4}
$