Y=(5x+2)(5x-4)

Solution for Y=(5x+2)(5x-4) equation:

=(5Y+2)(5Y-4)

We move all terms to the left:

-((5Y+2)(5Y-4))=0

We multiply parentheses ..

-((+25Y^2-20Y+10Y-8))=0


We calculate terms in parentheses: -((+25Y^2-20Y+10Y-8)), so:

(+25Y^2-20Y+10Y-8)

We get rid of parentheses

25Y^2-20Y+10Y-8

We add all the numbers together, and all the variables

25Y^2-10Y-8

Back to the equation:

-(25Y^2-10Y-8)


We get rid of parentheses

-25Y^2+10Y+8=0

a = -25; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-25)·8
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*-25}=\frac{-40}{-50}
=4/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*-25}=\frac{20}{-50}
=-2/5
$