Y=5(2x-1)(x+3)

Solution for Y=5(2x-1)(x+3) equation:

=5(2Y-1)(Y+3)

We move all terms to the left:

-(5(2Y-1)(Y+3))=0

We multiply parentheses ..

-(5(+2Y^2+6Y-1Y-3))=0


We calculate terms in parentheses: -(5(+2Y^2+6Y-1Y-3)), so:

5(+2Y^2+6Y-1Y-3)

We multiply parentheses

10Y^2+30Y-5Y-15

We add all the numbers together, and all the variables

10Y^2+25Y-15

Back to the equation:

-(10Y^2+25Y-15)


We get rid of parentheses

-10Y^2-25Y+15=0

a = -10; b = -25; c = +15;
Δ = b2-4ac
Δ = -252-4·(-10)·15
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-35}{2*-10}=\frac{-10}{-20}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+35}{2*-10}=\frac{60}{-20}
=-3
$