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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+8x-48x+3=0

We add all the numbers together, and all the variables

-8x^2-40x+3=0

a = -8; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-8)·3
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*-8}=\frac{40-4\sqrt{106}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*-8}=\frac{40+4\sqrt{106}}{-16}
$