(16/9x)*2+x*x=729

Solution for (16/9x)*2+x*x=729 equation:

(16/9x)*2+x*x=729

We move all terms to the left:

(16/9x)*2+x*x-(729)=0


Domain of the equation: 9x)*2!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+16/9x)*2+x*x-729=0

We multiply parentheses

32x+x*x-729=0

Wy multiply elements

x^2+32x-729=0

a = 1; b = 32; c = -729;
Δ = b2-4ac
Δ = 322-4·1·(-729)
Δ = 3940
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:

$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{985}}{2*1}=\frac{-32-2\sqrt{985}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{985}}{2*1}=\frac{-32+2\sqrt{985}}{2}
$