1/2x+3=4x+4

Solution for 1/2x+3=4x+4 equation:

1/2x+3=4x+4

We move all terms to the left:

1/2x+3-(4x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x-4+3=0

We multiply all the terms by the denominator


-4x*2x-4*2x+3*2x+1=0

Wy multiply elements

-8x^2-8x+6x+1=0

We add all the numbers together, and all the variables

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

a = -8; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-8)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-8}=\frac{-4}{-16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-8}=\frac{8}{-16}
=-1/2
$