5x-5/6x=50

Solution for 5x-5/6x=50 equation:

5x-5/6x=50

We move all terms to the left:

5x-5/6x-(50)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


5x*6x-50*6x-5=0

Wy multiply elements

30x^2-300x-5=0

a = 30; b = -300; c = -5;
Δ = b2-4ac
Δ = -3002-4·30·(-5)
Δ = 90600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{90600}=\sqrt{100*906}=\sqrt{100}*\sqrt{906}=10\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-10\sqrt{906}}{2*30}=\frac{300-10\sqrt{906}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+10\sqrt{906}}{2*30}=\frac{300+10\sqrt{906}}{60}
$