-17y+15y^2+4=3y-1

Solution for -17y+15y^2+4=3y-1 equation:

-17y+15y^2+4=3y-1

We move all terms to the left:

-17y+15y^2+4-(3y-1)=0

We get rid of parentheses

15y^2-17y-3y+1+4=0

We add all the numbers together, and all the variables

15y^2-20y+5=0

a = 15; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·15·5
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*15}=\frac{10}{30}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*15}=\frac{30}{30}
=1
$