81/2x+120=16x

Solution for 81/2x+120=16x equation:

81/2x+120=16x

We move all terms to the left:

81/2x+120-(16x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-16x+81/2x+120=0

We multiply all the terms by the denominator


-16x*2x+120*2x+81=0

Wy multiply elements

-32x^2+240x+81=0

a = -32; b = 240; c = +81;
Δ = b2-4ac
Δ = 2402-4·(-32)·81
Δ = 67968
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:

$\sqrt{\Delta}=\sqrt{67968}=\sqrt{576*118}=\sqrt{576}*\sqrt{118}=24\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-24\sqrt{118}}{2*-32}=\frac{-240-24\sqrt{118}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+24\sqrt{118}}{2*-32}=\frac{-240+24\sqrt{118}}{-64}
$