8^2-112x+360=8(x-9)(x-5)

Solution for 8^2-112x+360=8(x-9)(x-5) equation:

8^2-112x+360=8(x-9)(x-5)

We move all terms to the left:

8^2-112x+360-(8(x-9)(x-5))=0

We add all the numbers together, and all the variables

-112x-(8(x-9)(x-5))+424=0

We multiply parentheses ..

-(8(+x^2-5x-9x+45))-112x+424=0


We calculate terms in parentheses: -(8(+x^2-5x-9x+45)), so:

8(+x^2-5x-9x+45)

We multiply parentheses

8x^2-40x-72x+360

We add all the numbers together, and all the variables

8x^2-112x+360

Back to the equation:

-(8x^2-112x+360)


We add all the numbers together, and all the variables

-112x-(8x^2-112x+360)+424=0

We get rid of parentheses

-8x^2-112x+112x-360+424=0

We add all the numbers together, and all the variables

-8x^2+64=0

a = -8; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-8)·64
Δ = 2048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*-8}=\frac{0-32\sqrt{2}}{-16}
=-\frac{32\sqrt{2}}{-16}
=-\frac{2\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*-8}=\frac{0+32\sqrt{2}}{-16}
=\frac{32\sqrt{2}}{-16}
=\frac{2\sqrt{2}}{-1}
$