2x+8/9x=52

Solution for 2x+8/9x=52 equation:

2x+8/9x=52

We move all terms to the left:

2x+8/9x-(52)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


2x*9x-52*9x+8=0

Wy multiply elements

18x^2-468x+8=0

a = 18; b = -468; c = +8;
Δ = b2-4ac
Δ = -4682-4·18·8
Δ = 218448
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:

$\sqrt{\Delta}=\sqrt{218448}=\sqrt{144*1517}=\sqrt{144}*\sqrt{1517}=12\sqrt{1517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-12\sqrt{1517}}{2*18}=\frac{468-12\sqrt{1517}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+12\sqrt{1517}}{2*18}=\frac{468+12\sqrt{1517}}{36}
$