5x-3/x-6=5

Solution for 5x-3/x-6=5 equation:

5x-3/x-6=5

We move all terms to the left:

5x-3/x-6-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-3/x-11=0

We multiply all the terms by the denominator


5x*x-11*x-3=0

We add all the numbers together, and all the variables

-11x+5x*x-3=0

Wy multiply elements

5x^2-11x-3=0

a = 5; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·5·(-3)
Δ = 181
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{-(-11)-\sqrt{181}}{2*5}=\frac{11-\sqrt{181}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*5}=\frac{11+\sqrt{181}}{10}
$