/2x-4x+6-3=x-12

Solution for /2x-4x+6-3=x-12 equation:

/2x-4x+6-3=x-12

We move all terms to the left:

/2x-4x+6-3-(x-12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+/2x-(x-12)+3=0

We get rid of parentheses

-4x+/2x-x+12+3=0

We multiply all the terms by the denominator


-4x*2x-x*2x+12*2x+3*2x+=0

We add all the numbers together, and all the variables

-4x*2x-x*2x+12*2x+3*2x=0

Wy multiply elements

-8x^2-2x^2+24x+6x=0

We add all the numbers together, and all the variables

-10x^2+30x=0

a = -10; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-10)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-10}=\frac{-60}{-20}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-10}=\frac{0}{-20}
=0
$