3x+8/9x=4=3/8

Solution for 3x+8/9x=4=3/8 equation:

3x+8/9x=4=3/8

We move all terms to the left:

3x+8/9x-(4)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


3x*9x-4*9x+8=0

Wy multiply elements

27x^2-36x+8=0

a = 27; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·27·8
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{3}}{2*27}=\frac{36-12\sqrt{3}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{3}}{2*27}=\frac{36+12\sqrt{3}}{54}
$