1/2r+8=4-6r

Solution for 1/2r+8=4-6r equation:

1/2r+8=4-6r

We move all terms to the left:

1/2r+8-(4-6r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

1/2r-(-6r+4)+8=0

We get rid of parentheses

1/2r+6r-4+8=0

We multiply all the terms by the denominator


6r*2r-4*2r+8*2r+1=0

Wy multiply elements

12r^2-8r+16r+1=0

We add all the numbers together, and all the variables

12r^2+8r+1=0

a = 12; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·12·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*12}=\frac{-12}{24}
=-1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*12}=\frac{-4}{24}
=-1/6
$