0.6y+1=1/4y-15

Solution for 0.6y+1=1/4y-15 equation:

0.6y+1=1/4y-15

We move all terms to the left:

0.6y+1-(1/4y-15)=0


Domain of the equation: 4y-15)!=0

y∈R


We get rid of parentheses

0.6y-1/4y+15+1=0

We multiply all the terms by the denominator


(0.6y)*4y+15*4y+1*4y-1=0

We add all the numbers together, and all the variables

(+0.6y)*4y+15*4y+1*4y-1=0

We multiply parentheses

0y^2+15*4y+1*4y-1=0

Wy multiply elements

0y^2+60y+4y-1=0

We add all the numbers together, and all the variables

y^2+64y-1=0

a = 1; b = 64; c = -1;
Δ = b2-4ac
Δ = 642-4·1·(-1)
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-10\sqrt{41}}{2*1}=\frac{-64-10\sqrt{41}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+10\sqrt{41}}{2*1}=\frac{-64+10\sqrt{41}}{2}
$