4(r)-18=20+1/5(r)

Solution for 4(r)-18=20+1/5(r) equation:

4(r)-18=20+1/5(r)

We move all terms to the left:

4(r)-18-(20+1/5(r))=0


Domain of the equation: 5r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

4r-(1/5r+20)-18=0

We get rid of parentheses

4r-1/5r-20-18=0

We multiply all the terms by the denominator


4r*5r-20*5r-18*5r-1=0

Wy multiply elements

20r^2-100r-90r-1=0

We add all the numbers together, and all the variables

20r^2-190r-1=0

a = 20; b = -190; c = -1;
Δ = b2-4ac
Δ = -1902-4·20·(-1)
Δ = 36180
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:

$\sqrt{\Delta}=\sqrt{36180}=\sqrt{36*1005}=\sqrt{36}*\sqrt{1005}=6\sqrt{1005}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-6\sqrt{1005}}{2*20}=\frac{190-6\sqrt{1005}}{40}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+6\sqrt{1005}}{2*20}=\frac{190+6\sqrt{1005}}{40}
$