Y=(x-60)(2x+130)

Solution for Y=(x-60)(2x+130) equation:

=(Y-60)(2Y+130)

We move all terms to the left:

-((Y-60)(2Y+130))=0

We multiply parentheses ..

-((+2Y^2+130Y-120Y-7800))=0


We calculate terms in parentheses: -((+2Y^2+130Y-120Y-7800)), so:

(+2Y^2+130Y-120Y-7800)

We get rid of parentheses

2Y^2+130Y-120Y-7800

We add all the numbers together, and all the variables

2Y^2+10Y-7800

Back to the equation:

-(2Y^2+10Y-7800)


We get rid of parentheses

-2Y^2-10Y+7800=0

a = -2; b = -10; c = +7800;
Δ = b2-4ac
Δ = -102-4·(-2)·7800
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-250}{2*-2}=\frac{-240}{-4}
=+60
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+250}{2*-2}=\frac{260}{-4}
=-65
$