1/5x-2+5/6x=29

Solution for 1/5x-2+5/6x=29 equation:

1/5x-2+5/6x=29

We move all terms to the left:

1/5x-2+5/6x-(29)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+5/6x-31=0

We calculate fractions


6x/30x^2+25x/30x^2-31=0

We multiply all the terms by the denominator


6x+25x-31*30x^2=0

We add all the numbers together, and all the variables

31x-31*30x^2=0

Wy multiply elements

-930x^2+31x=0

a = -930; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-930)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-930}=\frac{-62}{-1860}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-930}=\frac{0}{-1860}
=0
$