Y=(4y^2+9y-1)-(2y^2+9)

Solution for Y=(4y^2+9y-1)-(2y^2+9) equation:

=(4Y^2+9Y-1)-(2Y^2+9)

We move all terms to the left:

-((4Y^2+9Y-1)-(2Y^2+9))=0


We calculate terms in parentheses: -((4Y^2+9Y-1)-(2Y^2+9)), so:

(4Y^2+9Y-1)-(2Y^2+9)

We get rid of parentheses

4Y^2-2Y^2+9Y-1-9

We add all the numbers together, and all the variables

2Y^2+9Y-10

Back to the equation:

-(2Y^2+9Y-10)


We get rid of parentheses

-2Y^2-9Y+10=0

a = -2; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·(-2)·10
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{161}}{2*-2}=\frac{9-\sqrt{161}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*-2}=\frac{9+\sqrt{161}}{-4}
$