1/2r+5=4r

Solution for 1/2r+5=4r equation:

1/2r+5=4r

We move all terms to the left:

1/2r+5-(4r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

-4r+1/2r+5=0

We multiply all the terms by the denominator


-4r*2r+5*2r+1=0

Wy multiply elements

-8r^2+10r+1=0

a = -8; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-8)·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*-8}=\frac{-10-2\sqrt{33}}{-16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*-8}=\frac{-10+2\sqrt{33}}{-16}
$