Y=(x+4)(x+10)

Solution for Y=(x+4)(x+10) equation:

=(Y+4)(Y+10)

We move all terms to the left:

-((Y+4)(Y+10))=0

We multiply parentheses ..

-((+Y^2+10Y+4Y+40))=0


We calculate terms in parentheses: -((+Y^2+10Y+4Y+40)), so:

(+Y^2+10Y+4Y+40)

We get rid of parentheses

Y^2+10Y+4Y+40

We add all the numbers together, and all the variables

Y^2+14Y+40

Back to the equation:

-(Y^2+14Y+40)


We get rid of parentheses

-Y^2-14Y-40=0

We add all the numbers together, and all the variables

-1Y^2-14Y-40=0

a = -1; b = -14; c = -40;
Δ = b2-4ac
Δ = -142-4·(-1)·(-40)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*-1}=\frac{8}{-2}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*-1}=\frac{20}{-2}
=-10
$