(1/6(y))-(y)=25

Solution for (1/6(y))-(y)=25 equation:

(1/6(y))-(y)=25

We move all terms to the left:

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


Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-1y+1/6y-25=0

We multiply all the terms by the denominator


-1y*6y-25*6y+1=0

Wy multiply elements

-6y^2-150y+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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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