Y=(6x+5)(5x-4)

Solution for Y=(6x+5)(5x-4) equation:

=(6Y+5)(5Y-4)

We move all terms to the left:

-((6Y+5)(5Y-4))=0

We multiply parentheses ..

-((+30Y^2-24Y+25Y-20))=0


We calculate terms in parentheses: -((+30Y^2-24Y+25Y-20)), so:

(+30Y^2-24Y+25Y-20)

We get rid of parentheses

30Y^2-24Y+25Y-20

We add all the numbers together, and all the variables

30Y^2+Y-20

Back to the equation:

-(30Y^2+Y-20)


We get rid of parentheses

-30Y^2-Y+20=0

We add all the numbers together, and all the variables

-30Y^2-1Y+20=0

a = -30; b = -1; c = +20;
Δ = b2-4ac
Δ = -12-4·(-30)·20
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*-30}=\frac{-48}{-60}
=4/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*-30}=\frac{50}{-60}
=-5/6
$