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+10)-12=0

We get rid of parentheses

3/4x+2x-10-12=0

We multiply all the terms by the denominator


2x*4x-10*4x-12*4x+3=0

Wy multiply elements

8x^2-40x-48x+3=0

We add all the numbers together, and all the variables

8x^2-88x+3=0

a = 8; b = -88; c = +3;
Δ = b2-4ac
Δ = -882-4·8·3
Δ = 7648
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:

$\sqrt{\Delta}=\sqrt{7648}=\sqrt{16*478}=\sqrt{16}*\sqrt{478}=4\sqrt{478}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{478}}{2*8}=\frac{88-4\sqrt{478}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{478}}{2*8}=\frac{88+4\sqrt{478}}{16}
$