10x-26/3x=-1

Solution for 10x-26/3x=-1 equation:

10x-26/3x=-1

We move all terms to the left:

10x-26/3x-(-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

10x-26/3x+1=0

We multiply all the terms by the denominator


10x*3x+1*3x-26=0

Wy multiply elements

30x^2+3x-26=0

a = 30; b = 3; c = -26;
Δ = b2-4ac
Δ = 32-4·30·(-26)
Δ = 3129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{3129}}{2*30}=\frac{-3-\sqrt{3129}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{3129}}{2*30}=\frac{-3+\sqrt{3129}}{60}
$