3y+4=1/5y-10

Solution for 3y+4=1/5y-10 equation:

3y+4=1/5y-10

We move all terms to the left:

3y+4-(1/5y-10)=0


Domain of the equation: 5y-10)!=0

y∈R


We get rid of parentheses

3y-1/5y+10+4=0

We multiply all the terms by the denominator


3y*5y+10*5y+4*5y-1=0

Wy multiply elements

15y^2+50y+20y-1=0

We add all the numbers together, and all the variables

15y^2+70y-1=0

a = 15; b = 70; c = -1;
Δ = b2-4ac
Δ = 702-4·15·(-1)
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-4\sqrt{310}}{2*15}=\frac{-70-4\sqrt{310}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+4\sqrt{310}}{2*15}=\frac{-70+4\sqrt{310}}{30}
$