5y-3/2y+1=25

Solution for 5y-3/2y+1=25 equation:

5y-3/2y+1=25

We move all terms to the left:

5y-3/2y+1-(25)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

5y-3/2y-24=0

We multiply all the terms by the denominator


5y*2y-24*2y-3=0

Wy multiply elements

10y^2-48y-3=0

a = 10; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·10·(-3)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{606}}{2*10}=\frac{48-2\sqrt{606}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{606}}{2*10}=\frac{48+2\sqrt{606}}{20}
$