x-5/6x=10

Solution for x-5/6x=10 equation:

x-5/6x=10

We move all terms to the left:

x-5/6x-(10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-10*6x-5=0

Wy multiply elements

6x^2-60x-5=0

a = 6; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·6·(-5)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{930}}{2*6}=\frac{60-2\sqrt{930}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{930}}{2*6}=\frac{60+2\sqrt{930}}{12}
$