3y=2*(-34/5)-2y-152

Solution for 3y=2*(-34/5)-2y-152 equation:

3y=2(-34/5)-2y-152

We move all terms to the left:

3y-(2(-34/5)-2y-152)=0


Domain of the equation: 5)-2y-152)!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


3y*5)-2y-152)-(2(-34=0

Wy multiply elements

15y^2-34=0

a = 15; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·15·(-34)
Δ = 2040
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:

$\sqrt{\Delta}=\sqrt{2040}=\sqrt{4*510}=\sqrt{4}*\sqrt{510}=2\sqrt{510}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{510}}{2*15}=\frac{0-2\sqrt{510}}{30}
=-\frac{2\sqrt{510}}{30}
=-\frac{\sqrt{510}}{15}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{510}}{2*15}=\frac{0+2\sqrt{510}}{30}
=\frac{2\sqrt{510}}{30}
=\frac{\sqrt{510}}{15}
$