-5y(y-16)=y+(-71)

Solution for -5y(y-16)=y+(-71) equation:

-5y(y-16)=y+(-71)

We move all terms to the left:

-5y(y-16)-(y+(-71))=0

We multiply parentheses

-5y^2+80y-(y+(-71))=0


We calculate terms in parentheses: -(y+(-71)), so:

y+(-71)

We add all the numbers together, and all the variables

y-71

Back to the equation:

-(y-71)


We get rid of parentheses

-5y^2+80y-y+71=0

We add all the numbers together, and all the variables

-5y^2+79y+71=0

a = -5; b = 79; c = +71;
Δ = b2-4ac
Δ = 792-4·(-5)·71
Δ = 7661
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{-(79)-\sqrt{7661}}{2*-5}=\frac{-79-\sqrt{7661}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+\sqrt{7661}}{2*-5}=\frac{-79+\sqrt{7661}}{-10}
$