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25+y=1/2y-3
We move all terms to the left:
25+y-(1/2y-3)=0
Domain of the equation: 2y-3)!=0We get rid of parentheses
y∈R
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} $
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