0=-1/2x+16x-96

Solution for 0=-1/2x+16x-96 equation:

0=-1/2x+16x-96

We move all terms to the left:

0-(-1/2x+16x-96)=0


Domain of the equation: 2x+16x-96)!=0

x∈R


We add all the numbers together, and all the variables

-(16x-1/2x-96)+0=0

We add all the numbers together, and all the variables

-(16x-1/2x-96)=0

We get rid of parentheses

-16x+1/2x+96=0

We multiply all the terms by the denominator


-16x*2x+96*2x+1=0

Wy multiply elements

-32x^2+192x+1=0

a = -32; b = 192; c = +1;
Δ = b2-4ac
Δ = 1922-4·(-32)·1
Δ = 36992
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:

$\sqrt{\Delta}=\sqrt{36992}=\sqrt{18496*2}=\sqrt{18496}*\sqrt{2}=136\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-136\sqrt{2}}{2*-32}=\frac{-192-136\sqrt{2}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+136\sqrt{2}}{2*-32}=\frac{-192+136\sqrt{2}}{-64}
$