(1/2)4x-9=32x

Solution for (1/2)4x-9=32x equation:

(1/2)4x-9=32x

We move all terms to the left:

(1/2)4x-9-(32x)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)4x-32x-9=0

We add all the numbers together, and all the variables

-32x+(+1/2)4x-9=0

We multiply parentheses

4x^2-32x-9=0

a = 4; b = -32; c = -9;
Δ = b2-4ac
Δ = -322-4·4·(-9)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{73}}{2*4}=\frac{32-4\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{73}}{2*4}=\frac{32+4\sqrt{73}}{8}
$