-2y(y-9)=-7y-27

Solution for -2y(y-9)=-7y-27 equation:

-2y(y-9)=-7y-27

We move all terms to the left:

-2y(y-9)-(-7y-27)=0

We multiply parentheses

-2y^2+18y-(-7y-27)=0

We get rid of parentheses

-2y^2+18y+7y+27=0

We add all the numbers together, and all the variables

-2y^2+25y+27=0

a = -2; b = 25; c = +27;
Δ = b2-4ac
Δ = 252-4·(-2)·27
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-29}{2*-2}=\frac{-54}{-4}
=13+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+29}{2*-2}=\frac{4}{-4}
=-1
$