3.1+7.5x-6.1=-2x-2+17/2x

Solution for 3.1+7.5x-6.1=-2x-2+17/2x equation:

3.1+7.5x-6.1=-2x-2+17/2x

We move all terms to the left:

3.1+7.5x-6.1-(-2x-2+17/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7.5x-(-2x+17/2x-2)+3.1-6.1=0

We add all the numbers together, and all the variables

7.5x-(-2x+17/2x-2)-3=0

We get rid of parentheses

7.5x+2x-17/2x+2-3=0

We multiply all the terms by the denominator


(7.5x)*2x+2x*2x+2*2x-3*2x-17=0

We add all the numbers together, and all the variables

(+7.5x)*2x+2x*2x+2*2x-3*2x-17=0

We multiply parentheses

14x^2+2x*2x+2*2x-3*2x-17=0

Wy multiply elements

14x^2+4x^2+4x-6x-17=0

We add all the numbers together, and all the variables

18x^2-2x-17=0

a = 18; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·18·(-17)
Δ = 1228
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:

$\sqrt{\Delta}=\sqrt{1228}=\sqrt{4*307}=\sqrt{4}*\sqrt{307}=2\sqrt{307}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{307}}{2*18}=\frac{2-2\sqrt{307}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{307}}{2*18}=\frac{2+2\sqrt{307}}{36}
$