1/6y=y-25

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

1/6y=y-25

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

1/6y-y+25=0

We multiply all the terms by the denominator


-y*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}
$