2r^2/2r-1+15r-8/2r-1=0

Solution for 2r^2/2r-1+15r-8/2r-1=0 equation:

2r^2/2r-1+15r-8/2r-1=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

2r^2/2r+15r-8/2r-2=0

We multiply all the terms by the denominator


2r^2+15r*2r-2*2r-8=0

Wy multiply elements

2r^2+30r^2-4r-8=0

We add all the numbers together, and all the variables

32r^2-4r-8=0

a = 32; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·32·(-8)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{65}}{2*32}=\frac{4-4\sqrt{65}}{64}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{65}}{2*32}=\frac{4+4\sqrt{65}}{64}
$