7=y(3y-13)

Solution for 7=y(3y-13) equation:

7=y(3y-13)

We move all terms to the left:

7-(y(3y-13))=0


We calculate terms in parentheses: -(y(3y-13)), so:

y(3y-13)

We multiply parentheses

3y^2-13y

Back to the equation:

-(3y^2-13y)


We get rid of parentheses

-3y^2+13y+7=0

a = -3; b = 13; c = +7;
Δ = b2-4ac
Δ = 132-4·(-3)·7
Δ = 253
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{-(13)-\sqrt{253}}{2*-3}=\frac{-13-\sqrt{253}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{253}}{2*-3}=\frac{-13+\sqrt{253}}{-6}
$