2x-10=39/5x-3

Solution for 2x-10=39/5x-3 equation:

2x-10=39/5x-3

We move all terms to the left:

2x-10-(39/5x-3)=0


Domain of the equation: 5x-3)!=0

x∈R


We get rid of parentheses

2x-39/5x+3-10=0

We multiply all the terms by the denominator


2x*5x+3*5x-10*5x-39=0

Wy multiply elements

10x^2+15x-50x-39=0

We add all the numbers together, and all the variables

10x^2-35x-39=0

a = 10; b = -35; c = -39;
Δ = b2-4ac
Δ = -352-4·10·(-39)
Δ = 2785
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{-(-35)-\sqrt{2785}}{2*10}=\frac{35-\sqrt{2785}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2785}}{2*10}=\frac{35+\sqrt{2785}}{20}
$