Y=(4x-1)(x+7)

Solution for Y=(4x-1)(x+7) equation:

=(4Y-1)(Y+7)

We move all terms to the left:

-((4Y-1)(Y+7))=0

We multiply parentheses ..

-((+4Y^2+28Y-1Y-7))=0


We calculate terms in parentheses: -((+4Y^2+28Y-1Y-7)), so:

(+4Y^2+28Y-1Y-7)

We get rid of parentheses

4Y^2+28Y-1Y-7

We add all the numbers together, and all the variables

4Y^2+27Y-7

Back to the equation:

-(4Y^2+27Y-7)


We get rid of parentheses

-4Y^2-27Y+7=0

a = -4; b = -27; c = +7;
Δ = b2-4ac
Δ = -272-4·(-4)·7
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-29}{2*-4}=\frac{-2}{-8}
=1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+29}{2*-4}=\frac{56}{-8}
=-7
$