Y=(2x-7)(5x+9)

Solution for Y=(2x-7)(5x+9) equation:

=(2Y-7)(5Y+9)

We move all terms to the left:

-((2Y-7)(5Y+9))=0

We multiply parentheses ..

-((+10Y^2+18Y-35Y-63))=0


We calculate terms in parentheses: -((+10Y^2+18Y-35Y-63)), so:

(+10Y^2+18Y-35Y-63)

We get rid of parentheses

10Y^2+18Y-35Y-63

We add all the numbers together, and all the variables

10Y^2-17Y-63

Back to the equation:

-(10Y^2-17Y-63)


We get rid of parentheses

-10Y^2+17Y+63=0

a = -10; b = 17; c = +63;
Δ = b2-4ac
Δ = 172-4·(-10)·63
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-53}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+53}{2*-10}=\frac{36}{-20}
=-1+4/5
$