5y-1/2y+3=6

Solution for 5y-1/2y+3=6 equation:

5y-1/2y+3=6

We move all terms to the left:

5y-1/2y+3-(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

5y-1/2y-3=0

We multiply all the terms by the denominator


5y*2y-3*2y-1=0

Wy multiply elements

10y^2-6y-1=0

a = 10; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·10·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*10}=\frac{6-2\sqrt{19}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*10}=\frac{6+2\sqrt{19}}{20}
$