/2x+6=3x-8.

Solution for /2x+6=3x-8. equation:

/2x+6=3x-8.

We move all terms to the left:

/2x+6-(3x-8.)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

/2x-(3x-8)+6=0

We get rid of parentheses

/2x-3x+8+6=0

We multiply all the terms by the denominator


-3x*2x+8*2x+6*2x+=0

We add all the numbers together, and all the variables

-3x*2x+8*2x+6*2x=0

Wy multiply elements

-6x^2+16x+12x=0

We add all the numbers together, and all the variables

-6x^2+28x=0

a = -6; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-6)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-6}=\frac{-56}{-12}
=4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-6}=\frac{0}{-12}
=0
$