25+y=1/2y-3

Solution for 25+y=1/2y-3 equation:

25+y=1/2y-3

We move all terms to the left:

25+y-(1/2y-3)=0


Domain of the equation: 2y-3)!=0

y∈R


We get rid of parentheses

y-1/2y+3+25=0

We multiply all the terms by the denominator


y*2y+3*2y+25*2y-1=0

Wy multiply elements

2y^2+6y+50y-1=0

We add all the numbers together, and all the variables

2y^2+56y-1=0

a = 2; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·2·(-1)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{786}}{2*2}=\frac{-56-2\sqrt{786}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{786}}{2*2}=\frac{-56+2\sqrt{786}}{4}
$