Y=7(x-5)(x-8)

Solution for Y=7(x-5)(x-8) equation:

=7(Y-5)(Y-8)

We move all terms to the left:

-(7(Y-5)(Y-8))=0

We multiply parentheses ..

-(7(+Y^2-8Y-5Y+40))=0


We calculate terms in parentheses: -(7(+Y^2-8Y-5Y+40)), so:

7(+Y^2-8Y-5Y+40)

We multiply parentheses

7Y^2-56Y-35Y+280

We add all the numbers together, and all the variables

7Y^2-91Y+280

Back to the equation:

-(7Y^2-91Y+280)


We get rid of parentheses

-7Y^2+91Y-280=0

a = -7; b = 91; c = -280;
Δ = b2-4ac
Δ = 912-4·(-7)·(-280)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-21}{2*-7}=\frac{-112}{-14}
=+8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+21}{2*-7}=\frac{-70}{-14}
=+5
$