1/4*4r-8=r-2

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

1/4*4r-8=r-2

We move all terms to the left:

1/4*4r-8-(r-2)=0


Domain of the equation: 4*4r!=0

r!=0/1

r!=0

r∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16r^2*4+32r*4-128r*4+1=0

Wy multiply elements

-64r^2+128r-512r+1=0

We add all the numbers together, and all the variables

-64r^2-384r+1=0

a = -64; b = -384; c = +1;
Δ = b2-4ac
Δ = -3842-4·(-64)·1
Δ = 147712
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{147712}=\sqrt{256*577}=\sqrt{256}*\sqrt{577}=16\sqrt{577}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-16\sqrt{577}}{2*-64}=\frac{384-16\sqrt{577}}{-128}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+16\sqrt{577}}{2*-64}=\frac{384+16\sqrt{577}}{-128}
$