X/10x-1=5x+6

Solution for X/10x-1=5x+6 equation:

X/10X-1=5X+6

We move all terms to the left:

X/10X-1-(5X+6)=0


Domain of the equation: 10X!=0

X!=0/10

X!=0

X∈R


We get rid of parentheses

X/10X-5X-6-1=0

We multiply all the terms by the denominator


X-5X*10X-6*10X-1*10X=0

Wy multiply elements

-50X^2+X-60X-10X=0

We add all the numbers together, and all the variables

-50X^2-69X=0

a = -50; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·(-50)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*-50}=\frac{0}{-100}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*-50}=\frac{138}{-100}
=-1+19/50
$