2=y(52-3y)

Solution for 2=y(52-3y) equation:

2=y(52-3y)

We move all terms to the left:

2-(y(52-3y))=0

We add all the numbers together, and all the variables

-(y(-3y+52))+2=0


We calculate terms in parentheses: -(y(-3y+52)), so:

y(-3y+52)

We multiply parentheses

-3y^2+52y

Back to the equation:

-(-3y^2+52y)


We get rid of parentheses

3y^2-52y+2=0

a = 3; b = -52; c = +2;
Δ = b2-4ac
Δ = -522-4·3·2
Δ = 2680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2680}=\sqrt{4*670}=\sqrt{4}*\sqrt{670}=2\sqrt{670}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-2\sqrt{670}}{2*3}=\frac{52-2\sqrt{670}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+2\sqrt{670}}{2*3}=\frac{52+2\sqrt{670}}{6}
$