5y=3(5y)^2-1

Solution for 5y=3(5y)^2-1 equation:

5y=3(5y)^2-1

We move all terms to the left:

5y-(3(5y)^2-1)=0

We get rid of parentheses

-35y^2+5y+1=0

a = -35; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-35)·1
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{165}}{2*-35}=\frac{-5-\sqrt{165}}{-70}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{165}}{2*-35}=\frac{-5+\sqrt{165}}{-70}
$