3x+6/3x=10

Solution for 3x+6/3x=10 equation:

3x+6/3x=10

We move all terms to the left:

3x+6/3x-(10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-10*3x+6=0

Wy multiply elements

9x^2-30x+6=0

a = 9; b = -30; c = +6;
Δ = b2-4ac
Δ = -302-4·9·6
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{19}}{2*9}=\frac{30-6\sqrt{19}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{19}}{2*9}=\frac{30+6\sqrt{19}}{18}
$