3x+4/3x=30

Solution for 3x+4/3x=30 equation:

3x+4/3x=30

We move all terms to the left:

3x+4/3x-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-30*3x+4=0

Wy multiply elements

9x^2-90x+4=0

a = 9; b = -90; c = +4;
Δ = b2-4ac
Δ = -902-4·9·4
Δ = 7956
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:

$\sqrt{\Delta}=\sqrt{7956}=\sqrt{36*221}=\sqrt{36}*\sqrt{221}=6\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{221}}{2*9}=\frac{90-6\sqrt{221}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{221}}{2*9}=\frac{90+6\sqrt{221}}{18}
$