10r(2r-12)=1

Solution for 10r(2r-12)=1 equation:

10r(2r-12)=1

We move all terms to the left:

10r(2r-12)-(1)=0

We multiply parentheses

20r^2-120r-1=0

a = 20; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·20·(-1)
Δ = 14480
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:

$\sqrt{\Delta}=\sqrt{14480}=\sqrt{16*905}=\sqrt{16}*\sqrt{905}=4\sqrt{905}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{905}}{2*20}=\frac{120-4\sqrt{905}}{40}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{905}}{2*20}=\frac{120+4\sqrt{905}}{40}
$