(3x^2-6)/8-x=x-2

Solution for (3x^2-6)/8-x=x-2 equation:

(3x^2-6)/8-x=x-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(3x^2-6)/8-(x-2)=0

We get rid of parentheses

-1x+(3x^2-6)/8-x+2=0

We multiply all the terms by the denominator


-1x*8+(3x^2-6)-x*8+2*8=0

We add all the numbers together, and all the variables

-1x*8+(3x^2-6)-x*8+16=0

Wy multiply elements

-8x+(3x^2-6)-8x+16=0

We get rid of parentheses

3x^2-8x-8x-6+16=0

We add all the numbers together, and all the variables

3x^2-16x+10=0

a = 3; b = -16; c = +10;
Δ = b2-4ac
Δ = -162-4·3·10
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{34}}{2*3}=\frac{16-2\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{34}}{2*3}=\frac{16+2\sqrt{34}}{6}
$