3+5/2x-6=5x-3/2x

Solution for 3+5/2x-6=5x-3/2x equation:

3+5/2x-6=5x-3/2x

We move all terms to the left:

3+5/2x-6-(5x-3/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+5x-3/2x)+3-6=0

We add all the numbers together, and all the variables

5/2x-(+5x-3/2x)-3=0

We get rid of parentheses

5/2x-5x+3/2x-3=0

We multiply all the terms by the denominator


-5x*2x-3*2x+5+3=0

We add all the numbers together, and all the variables

-5x*2x-3*2x+8=0

Wy multiply elements

-10x^2-6x+8=0

a = -10; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-10)·8
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*-10}=\frac{6-2\sqrt{89}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*-10}=\frac{6+2\sqrt{89}}{-20}
$