X-25=1/6x

Solution for X-25=1/6x equation:

X-25=1/6X

We move all terms to the left:

X-25-(1/6X)=0


Domain of the equation: 6X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/6X)-25=0

We get rid of parentheses

X-1/6X-25=0

We multiply all the terms by the denominator


X*6X-25*6X-1=0

Wy multiply elements

6X^2-150X-1=0

a = 6; b = -150; c = -1;
Δ = b2-4ac
Δ = -1502-4·6·(-1)
Δ = 22524
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:

$\sqrt{\Delta}=\sqrt{22524}=\sqrt{4*5631}=\sqrt{4}*\sqrt{5631}=2\sqrt{5631}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5631}}{2*6}=\frac{150-2\sqrt{5631}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5631}}{2*6}=\frac{150+2\sqrt{5631}}{12}
$