3x+2/3x=77

Solution for 3x+2/3x=77 equation:

3x+2/3x=77

We move all terms to the left:

3x+2/3x-(77)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-77*3x+2=0

Wy multiply elements

9x^2-231x+2=0

a = 9; b = -231; c = +2;
Δ = b2-4ac
Δ = -2312-4·9·2
Δ = 53289
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:

$\sqrt{\Delta}=\sqrt{53289}=\sqrt{9*5921}=\sqrt{9}*\sqrt{5921}=3\sqrt{5921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-231)-3\sqrt{5921}}{2*9}=\frac{231-3\sqrt{5921}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-231)+3\sqrt{5921}}{2*9}=\frac{231+3\sqrt{5921}}{18}
$