(4x^2-30x+32)/((x-2)(x-4)^2)=0

Solution for (4x^2-30x+32)/((x-2)(x-4)^2)=0 equation:

(4x^2-30x+32)/((x-2)(x-4)^2)=0


Domain of the equation: ((x-2)(x-4)^2)!=0

x∈R


We multiply parentheses ..

(4x^2-30x+32)/((+x^2-4x-2x+8)^2)=0

We multiply all the terms by the denominator


(4x^2-30x+32)=0

We get rid of parentheses

4x^2-30x+32=0

a = 4; b = -30; c = +32;
Δ = b2-4ac
Δ = -302-4·4·32
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{97}}{2*4}=\frac{30-2\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{97}}{2*4}=\frac{30+2\sqrt{97}}{8}
$