3x+5/x-3=10

Solution for 3x+5/x-3=10 equation:

3x+5/x-3=10

We move all terms to the left:

3x+5/x-3-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+5/x-13=0

We multiply all the terms by the denominator


3x*x-13*x+5=0

We add all the numbers together, and all the variables

-13x+3x*x+5=0

Wy multiply elements

3x^2-13x+5=0

a = 3; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·3·5
Δ = 109
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{109}}{2*3}=\frac{13-\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{109}}{2*3}=\frac{13+\sqrt{109}}{6}
$