180=(y^2-5)+(-8y+165)

Solution for 180=(y^2-5)+(-8y+165) equation:

180=(y^2-5)+(-8y+165)

We move all terms to the left:

180-((y^2-5)+(-8y+165))=0


We calculate terms in parentheses: -((y^2-5)+(-8y+165)), so:

(y^2-5)+(-8y+165)

We get rid of parentheses

y^2-8y-5+165

We add all the numbers together, and all the variables

y^2-8y+160

Back to the equation:

-(y^2-8y+160)


We get rid of parentheses

-y^2+8y-160+180=0

We add all the numbers together, and all the variables

-1y^2+8y+20=0

a = -1; b = 8; c = +20;
Δ = b2-4ac
Δ = 82-4·(-1)·20
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*-1}=\frac{-20}{-2}
=+10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-1}=\frac{4}{-2}
=-2
$