5(2y/3+15)10y=-10

Solution for 5(2y/3+15)10y=-10 equation:

5(2y/3+15)10y=-10

We move all terms to the left:

5(2y/3+15)10y-(-10)=0


Domain of the equation: 3+15)10y!=0

We move all terms containing y to the left, all other terms to the right

15)10y!=-3

y!=-3/1

y!=-3

y∈R


We add all the numbers together, and all the variables

5(2y/3+15)10y+10=0

We multiply parentheses

100y^2+750y+10=0

a = 100; b = 750; c = +10;
Δ = b2-4ac
Δ = 7502-4·100·10
Δ = 558500
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:

$\sqrt{\Delta}=\sqrt{558500}=\sqrt{100*5585}=\sqrt{100}*\sqrt{5585}=10\sqrt{5585}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(750)-10\sqrt{5585}}{2*100}=\frac{-750-10\sqrt{5585}}{200}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(750)+10\sqrt{5585}}{2*100}=\frac{-750+10\sqrt{5585}}{200}
$