(-16x^2-80x+64)/(x-1)=0

Solution for (-16x^2-80x+64)/(x-1)=0 equation:

(-16x^2-80x+64)/(x-1)=0


Domain of the equation: (x-1)!=0

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We multiply all the terms by the denominator


(-16x^2-80x+64)=0

We get rid of parentheses

-16x^2-80x+64=0

a = -16; b = -80; c = +64;
Δ = b2-4ac
Δ = -802-4·(-16)·64
Δ = 10496
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:

$\sqrt{\Delta}=\sqrt{10496}=\sqrt{256*41}=\sqrt{256}*\sqrt{41}=16\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{41}}{2*-16}=\frac{80-16\sqrt{41}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{41}}{2*-16}=\frac{80+16\sqrt{41}}{-32}
$