5x=1/3x+10

Solution for 5x=1/3x+10 equation:

5x=1/3x+10

We move all terms to the left:

5x-(1/3x+10)=0


Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

5x-1/3x-10=0

We multiply all the terms by the denominator


5x*3x-10*3x-1=0

Wy multiply elements

15x^2-30x-1=0

a = 15; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·15·(-1)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{15}}{2*15}=\frac{30-8\sqrt{15}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{15}}{2*15}=\frac{30+8\sqrt{15}}{30}
$