6r^2-9r-5=1

Solution for 6r^2-9r-5=1 equation:

6r^2-9r-5=1

We move all terms to the left:

6r^2-9r-5-(1)=0

We add all the numbers together, and all the variables

6r^2-9r-6=0

a = 6; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·6·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*6}=\frac{-6}{12}
=-1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*6}=\frac{24}{12}
=2
$