1/2x+2=4x-6

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

1/2x+2=4x-6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+12x+4x+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}
$