Y=-(x-14)(x-5)

Solution for Y=-(x-14)(x-5) equation:

=-(Y-14)(Y-5)

We move all terms to the left:

-(-(Y-14)(Y-5))=0

We multiply parentheses ..

-(-(+Y^2-5Y-14Y+70))=0


We calculate terms in parentheses: -(-(+Y^2-5Y-14Y+70)), so:

-(+Y^2-5Y-14Y+70)

We get rid of parentheses

-Y^2+5Y+14Y-70

We add all the numbers together, and all the variables

-1Y^2+19Y-70

Back to the equation:

-(-1Y^2+19Y-70)


We get rid of parentheses

1Y^2-19Y+70=0

We add all the numbers together, and all the variables

Y^2-19Y+70=0

a = 1; b = -19; c = +70;
Δ = b2-4ac
Δ = -192-4·1·70
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{-(-19)-9}{2*1}=\frac{10}{2}
=5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+9}{2*1}=\frac{28}{2}
=14
$