Y=(2x+5)(x+6)

Solution for Y=(2x+5)(x+6) equation:

=(2Y+5)(Y+6)

We move all terms to the left:

-((2Y+5)(Y+6))=0

We multiply parentheses ..

-((+2Y^2+12Y+5Y+30))=0


We calculate terms in parentheses: -((+2Y^2+12Y+5Y+30)), so:

(+2Y^2+12Y+5Y+30)

We get rid of parentheses

2Y^2+12Y+5Y+30

We add all the numbers together, and all the variables

2Y^2+17Y+30

Back to the equation:

-(2Y^2+17Y+30)


We get rid of parentheses

-2Y^2-17Y-30=0

a = -2; b = -17; c = -30;
Δ = b2-4ac
Δ = -172-4·(-2)·(-30)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*-2}=\frac{10}{-4}
=-2+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*-2}=\frac{24}{-4}
=-6
$