-5=y(2y-11)

Solution for -5=y(2y-11) equation:

-5=y(2y-11)

We move all terms to the left:

-5-(y(2y-11))=0


We calculate terms in parentheses: -(y(2y-11)), so:

y(2y-11)

We multiply parentheses

2y^2-11y

Back to the equation:

-(2y^2-11y)


We get rid of parentheses

-2y^2+11y-5=0

a = -2; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-2)·(-5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-2}=\frac{-20}{-4}
=+5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-2}=\frac{-2}{-4}
=1/2
$