Y=(4-y)*(4-y)-14-6y

Solution for Y=(4-y)*(4-y)-14-6y equation:

=(4-Y)(4-Y)-14-6Y

We move all terms to the left:

-((4-Y)(4-Y)-14-6Y)=0

We add all the numbers together, and all the variables

-((-1Y+4)(-1Y+4)-14-6Y)=0

We multiply parentheses ..

-((+Y^2-4Y-4Y+16)-14-6Y)=0


We calculate terms in parentheses: -((+Y^2-4Y-4Y+16)-14-6Y), so:

(+Y^2-4Y-4Y+16)-14-6Y

determiningTheFunctionDomain
(+Y^2-4Y-4Y+16)-6Y-14

We get rid of parentheses

Y^2-4Y-4Y-6Y+16-14

We add all the numbers together, and all the variables

Y^2-14Y+2

Back to the equation:

-(Y^2-14Y+2)


We get rid of parentheses

-Y^2+14Y-2=0

We add all the numbers together, and all the variables

-1Y^2+14Y-2=0

a = -1; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·(-1)·(-2)
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{47}}{2*-1}=\frac{-14-2\sqrt{47}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{47}}{2*-1}=\frac{-14+2\sqrt{47}}{-2}
$