8x-10/13x-2x=1

Solution for 8x-10/13x-2x=1 equation:

8x-10/13x-2x=1

We move all terms to the left:

8x-10/13x-2x-(1)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

6x-10/13x-1=0

We multiply all the terms by the denominator


6x*13x-1*13x-10=0

Wy multiply elements

78x^2-13x-10=0

a = 78; b = -13; c = -10;
Δ = b2-4ac
Δ = -132-4·78·(-10)
Δ = 3289
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{-(-13)-\sqrt{3289}}{2*78}=\frac{13-\sqrt{3289}}{156}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{3289}}{2*78}=\frac{13+\sqrt{3289}}{156}
$