1/4r+17=r-4

Solution for 1/4r+17=r-4 equation:

1/4r+17=r-4

We move all terms to the left:

1/4r+17-(r-4)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R


We get rid of parentheses

1/4r-r+4+17=0

We multiply all the terms by the denominator


-r*4r+4*4r+17*4r+1=0

Wy multiply elements

-4r^2+16r+68r+1=0

We add all the numbers together, and all the variables

-4r^2+84r+1=0

a = -4; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-4)·1
Δ = 7072
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:

$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{442}}{2*-4}=\frac{-84-4\sqrt{442}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{442}}{2*-4}=\frac{-84+4\sqrt{442}}{-8}
$