15y-6+5=1/2y+5y+2

Solution for 15y-6+5=1/2y+5y+2 equation:

15y-6+5=1/2y+5y+2

We move all terms to the left:

15y-6+5-(1/2y+5y+2)=0


Domain of the equation: 2y+5y+2)!=0

y∈R


We add all the numbers together, and all the variables

15y-(5y+1/2y+2)-6+5=0

We add all the numbers together, and all the variables

15y-(5y+1/2y+2)-1=0

We get rid of parentheses

15y-5y-1/2y-2-1=0

We multiply all the terms by the denominator


15y*2y-5y*2y-2*2y-1*2y-1=0

Wy multiply elements

30y^2-10y^2-4y-2y-1=0

We add all the numbers together, and all the variables

20y^2-6y-1=0

a = 20; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·20·(-1)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*20}=\frac{6-2\sqrt{29}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*20}=\frac{6+2\sqrt{29}}{40}
$