4x+6=1/2x-2

Solution for 4x+6=1/2x-2 equation:

4x+6=1/2x-2

We move all terms to the left:

4x+6-(1/2x-2)=0


Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

4x-1/2x+2+6=0

We multiply all the terms by the denominator


4x*2x+2*2x+6*2x-1=0

Wy multiply elements

8x^2+4x+12x-1=0

We add all the numbers together, and all the variables

8x^2+16x-1=0

a = 8; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·8·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12\sqrt{2}}{2*8}=\frac{-16-12\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12\sqrt{2}}{2*8}=\frac{-16+12\sqrt{2}}{16}
$