4/5y-3y=-34

Solution for 4/5y-3y=-34 equation:

4/5y-3y=-34

We move all terms to the left:

4/5y-3y-(-34)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-3y+4/5y+34=0

We multiply all the terms by the denominator


-3y*5y+34*5y+4=0

Wy multiply elements

-15y^2+170y+4=0

a = -15; b = 170; c = +4;
Δ = b2-4ac
Δ = 1702-4·(-15)·4
Δ = 29140
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:

$\sqrt{\Delta}=\sqrt{29140}=\sqrt{4*7285}=\sqrt{4}*\sqrt{7285}=2\sqrt{7285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-2\sqrt{7285}}{2*-15}=\frac{-170-2\sqrt{7285}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+2\sqrt{7285}}{2*-15}=\frac{-170+2\sqrt{7285}}{-30}
$