41/2x+1/3x=58

Solution for 41/2x+1/3x=58 equation:

41/2x+1/3x=58

We move all terms to the left:

41/2x+1/3x-(58)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


123x/6x^2+2x/6x^2-58=0

We multiply all the terms by the denominator


123x+2x-58*6x^2=0

We add all the numbers together, and all the variables

125x-58*6x^2=0

Wy multiply elements

-348x^2+125x=0

a = -348; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-348)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-348}=\frac{-250}{-696}
=125/348
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-348}=\frac{0}{-696}
=0
$