/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: x!=0

x∈R


We get rid of parentheses

/x-5x-10-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-16x-5x*x=0

Wy multiply elements

-5x^2-16x=0

a = -5; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-5)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-5}=\frac{32}{-10}
=-3+1/5
$