6/3+4/2x=0,5x+17

Solution for 6/3+4/2x=0,5x+17 equation:

6/3+4/2x=0.5x+17

We move all terms to the left:

6/3+4/2x-(0.5x+17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/2x-(0.5x+17)+2=0

We get rid of parentheses

4/2x-0.5x-17+2=0

We multiply all the terms by the denominator


-(0.5x)*2x-17*2x+2*2x+4=0

We add all the numbers together, and all the variables

-(+0.5x)*2x-17*2x+2*2x+4=0

We multiply parentheses

-0x^2-17*2x+2*2x+4=0

Wy multiply elements

-0x^2-34x+4x+4=0

We add all the numbers together, and all the variables

-1x^2-30x+4=0

a = -1; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·(-1)·4
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*-1}=\frac{30-2\sqrt{229}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*-1}=\frac{30+2\sqrt{229}}{-2}
$