-8(x-21,5)(x-7,5)=-8^2+232x-1290

Solution for -8(x-21,5)(x-7,5)=-8^2+232x-1290 equation:

-8(x-21.5)(x-7.5)=-8^2+232x-1290

We move all terms to the left:

-8(x-21.5)(x-7.5)-(-8^2+232x-1290)=0

We get rid of parentheses

-8(x-21.5)(x-7.5)-232x+1290+8^2=0

We multiply parentheses ..

-8(+x^2-7.5x-21.5x+161.25)-232x+1290+8^2=0

We add all the numbers together, and all the variables

-8(+x^2-7.5x-21.5x+161.25)-232x+1354=0

We multiply parentheses

-8x^2+56x+168x-232x-1290+1354=0

We add all the numbers together, and all the variables

-8x^2-8x+64=0

a = -8; b = -8; c = +64;
Δ = b2-4ac
Δ = -82-4·(-8)·64
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{33}}{2*-8}=\frac{8-8\sqrt{33}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{33}}{2*-8}=\frac{8+8\sqrt{33}}{-16}
$