x^2-8x^2-x+32=0

Solution for x^2-8x^2-x+32=0 equation:

x^2-8x^2-x+32=0

We add all the numbers together, and all the variables

-7x^2-1x+32=0

a = -7; b = -1; c = +32;
Δ = b2-4ac
Δ = -12-4·(-7)·32
Δ = 897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{897}}{2*-7}=\frac{1-\sqrt{897}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{897}}{2*-7}=\frac{1+\sqrt{897}}{-14}
$