1/2y-40=20y+25

Solution for 1/2y-40=20y+25 equation:

1/2y-40=20y+25

We move all terms to the left:

1/2y-40-(20y+25)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-20y-25-40=0

We multiply all the terms by the denominator


-20y*2y-25*2y-40*2y+1=0

Wy multiply elements

-40y^2-50y-80y+1=0

We add all the numbers together, and all the variables

-40y^2-130y+1=0

a = -40; b = -130; c = +1;
Δ = b2-4ac
Δ = -1302-4·(-40)·1
Δ = 17060
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:

$\sqrt{\Delta}=\sqrt{17060}=\sqrt{4*4265}=\sqrt{4}*\sqrt{4265}=2\sqrt{4265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4265}}{2*-40}=\frac{130-2\sqrt{4265}}{-80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4265}}{2*-40}=\frac{130+2\sqrt{4265}}{-80}
$