2(y2-15)=y(y+10)

Solution for 2(y2-15)=y(y+10) equation:

2(y2-15)=y(y+10)

We move all terms to the left:

2(y2-15)-(y(y+10))=0

We add all the numbers together, and all the variables

2(+y^2-15)-(y(y+10))=0

We multiply parentheses

2y^2-(y(y+10))-30=0


We calculate terms in parentheses: -(y(y+10)), so:

y(y+10)

We multiply parentheses

y^2+10y

Back to the equation:

-(y^2+10y)


We get rid of parentheses

2y^2-y^2-10y-30=0

We add all the numbers together, and all the variables

y^2-10y-30=0

a = 1; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·1·(-30)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*1}=\frac{10-2\sqrt{55}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*1}=\frac{10+2\sqrt{55}}{2}
$