3x+4/3x=78

Solution for 3x+4/3x=78 equation:

3x+4/3x=78

We move all terms to the left:

3x+4/3x-(78)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-78*3x+4=0

Wy multiply elements

9x^2-234x+4=0

a = 9; b = -234; c = +4;
Δ = b2-4ac
Δ = -2342-4·9·4
Δ = 54612
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:

$\sqrt{\Delta}=\sqrt{54612}=\sqrt{36*1517}=\sqrt{36}*\sqrt{1517}=6\sqrt{1517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-6\sqrt{1517}}{2*9}=\frac{234-6\sqrt{1517}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+6\sqrt{1517}}{2*9}=\frac{234+6\sqrt{1517}}{18}
$