Y=2(x-7)(x+5)

Solution for Y=2(x-7)(x+5) equation:

=2(Y-7)(Y+5)

We move all terms to the left:

-(2(Y-7)(Y+5))=0

We multiply parentheses ..

-(2(+Y^2+5Y-7Y-35))=0


We calculate terms in parentheses: -(2(+Y^2+5Y-7Y-35)), so:

2(+Y^2+5Y-7Y-35)

We multiply parentheses

2Y^2+10Y-14Y-70

We add all the numbers together, and all the variables

2Y^2-4Y-70

Back to the equation:

-(2Y^2-4Y-70)


We get rid of parentheses

-2Y^2+4Y+70=0

a = -2; b = 4; c = +70;
Δ = b2-4ac
Δ = 42-4·(-2)·70
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-24}{2*-2}=\frac{-28}{-4}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+24}{2*-2}=\frac{20}{-4}
=-5
$