x-5=-6+3/2x

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

x-5=-6+3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*2x+6*2x-5*2x-3=0

Wy multiply elements

2x^2+12x-10x-3=0

We add all the numbers together, and all the variables

2x^2+2x-3=0

a = 2; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·2·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*2}=\frac{-2-2\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*2}=\frac{-2+2\sqrt{7}}{4}
$