5r^2-6r=-1

Solution for 5r^2-6r=-1 equation:

5r^2-6r=-1

We move all terms to the left:

5r^2-6r-(-1)=0

We add all the numbers together, and all the variables

5r^2-6r+1=0

a = 5; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·5·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*5}=\frac{2}{10}
=1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*5}=\frac{10}{10}
=1
$