4x-6+6=x+x-3+(x-3)/2

Solution for 4x-6+6=x+x-3+(x-3)/2 equation:

4x-6+6=x+x-3+(x-3)/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x-(x+x-3+(x-3)/2)=0

We multiply all the terms by the denominator


4x*2)-(x+x+(x-3)-3=0

We add all the numbers together, and all the variables

x+4x*2)-(x+(x-3)-3=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2+2x-6=0

a = 8; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·8·(-6)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*8}=\frac{12}{16}
=3/4
$