8/8*x+9*x=30

Solution for 8/8*x+9*x=30 equation:

8/8x+9x=30

We move all terms to the left:

8/8x+9x-(30)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

9x+8/8x-30=0

We multiply all the terms by the denominator


9x*8x-30*8x+8=0

Wy multiply elements

72x^2-240x+8=0

a = 72; b = -240; c = +8;
Δ = b2-4ac
Δ = -2402-4·72·8
Δ = 55296
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:

$\sqrt{\Delta}=\sqrt{55296}=\sqrt{9216*6}=\sqrt{9216}*\sqrt{6}=96\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-96\sqrt{6}}{2*72}=\frac{240-96\sqrt{6}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+96\sqrt{6}}{2*72}=\frac{240+96\sqrt{6}}{144}
$