15/2y-25+3y=-6

Solution for 15/2y-25+3y=-6 equation:

15/2y-25+3y=-6

We move all terms to the left:

15/2y-25+3y-(-6)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y+15/2y-19=0

We multiply all the terms by the denominator


3y*2y-19*2y+15=0

Wy multiply elements

6y^2-38y+15=0

a = 6; b = -38; c = +15;
Δ = b2-4ac
Δ = -382-4·6·15
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{271}}{2*6}=\frac{38-2\sqrt{271}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{271}}{2*6}=\frac{38+2\sqrt{271}}{12}
$