x-6/5x=10

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

x-6/5x=10

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-50x-6=0

a = 5; b = -50; c = -6;
Δ = b2-4ac
Δ = -502-4·5·(-6)
Δ = 2620
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:

$\sqrt{\Delta}=\sqrt{2620}=\sqrt{4*655}=\sqrt{4}*\sqrt{655}=2\sqrt{655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{655}}{2*5}=\frac{50-2\sqrt{655}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{655}}{2*5}=\frac{50+2\sqrt{655}}{10}
$