1/2x-2x+2=6x+5

Solution for 1/2x-2x+2=6x+5 equation:

1/2x-2x+2=6x+5

We move all terms to the left:

1/2x-2x+2-(6x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/2x-(6x+5)+2=0

We get rid of parentheses

-2x+1/2x-6x-5+2=0

We multiply all the terms by the denominator


-2x*2x-6x*2x-5*2x+2*2x+1=0

Wy multiply elements

-4x^2-12x^2-10x+4x+1=0

We add all the numbers together, and all the variables

-16x^2-6x+1=0

a = -16; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-16)·1
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-16}=\frac{-4}{-32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-16}=\frac{16}{-32}
=-1/2
$