6x-30/x-11=0

Solution for 6x-30/x-11=0 equation:

6x-30/x-11=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x-11*x-30=0

We add all the numbers together, and all the variables

-11x+6x*x-30=0

Wy multiply elements

6x^2-11x-30=0

a = 6; b = -11; c = -30;
Δ = b2-4ac
Δ = -112-4·6·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*6}=\frac{40}{12}
=3+1/3
$