6y-5y^2=1

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

6y-5y^2=1

We move all terms to the left:

6y-5y^2-(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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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