Y^2+6y+10=2y^2+6y-15

Solution for Y^2+6y+10=2y^2+6y-15 equation:

^2+6Y+10=2Y^2+6Y-15

We move all terms to the left:

^2+6Y+10-(2Y^2+6Y-15)=0

We add all the numbers together, and all the variables

6Y-(2Y^2+6Y-15)=0

We get rid of parentheses

-2Y^2+6Y-6Y+15=0

We add all the numbers together, and all the variables

-2Y^2+15=0

a = -2; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-2)·15
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-2}=\frac{0-2\sqrt{30}}{-4}
=-\frac{2\sqrt{30}}{-4}
=-\frac{\sqrt{30}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-2}=\frac{0+2\sqrt{30}}{-4}
=\frac{2\sqrt{30}}{-4}
=\frac{\sqrt{30}}{-2}
$