81/2x+180=16x

Solution for 81/2x+180=16x equation:

81/2x+180=16x

We move all terms to the left:

81/2x+180-(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+180=0

We multiply all the terms by the denominator


-16x*2x+180*2x+81=0

Wy multiply elements

-32x^2+360x+81=0

a = -32; b = 360; c = +81;
Δ = b2-4ac
Δ = 3602-4·(-32)·81
Δ = 139968
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:

$\sqrt{\Delta}=\sqrt{139968}=\sqrt{46656*3}=\sqrt{46656}*\sqrt{3}=216\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-216\sqrt{3}}{2*-32}=\frac{-360-216\sqrt{3}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+216\sqrt{3}}{2*-32}=\frac{-360+216\sqrt{3}}{-64}
$