1/3(8x)+5x=46

Solution for 1/3(8x)+5x=46 equation:

1/3(8x)+5x=46

We move all terms to the left:

1/3(8x)+5x-(46)=0


Domain of the equation: 38x!=0

x!=0/38

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/38x-46=0

We multiply all the terms by the denominator


5x*38x-46*38x+1=0

Wy multiply elements

190x^2-1748x+1=0

a = 190; b = -1748; c = +1;
Δ = b2-4ac
Δ = -17482-4·190·1
Δ = 3054744
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:

$\sqrt{\Delta}=\sqrt{3054744}=\sqrt{36*84854}=\sqrt{36}*\sqrt{84854}=6\sqrt{84854}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1748)-6\sqrt{84854}}{2*190}=\frac{1748-6\sqrt{84854}}{380}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1748)+6\sqrt{84854}}{2*190}=\frac{1748+6\sqrt{84854}}{380}
$