8y^2-5y+7=2y^2+7y+11

Solution for 8y^2-5y+7=2y^2+7y+11 equation:

8y^2-5y+7=2y^2+7y+11

We move all terms to the left:

8y^2-5y+7-(2y^2+7y+11)=0

We get rid of parentheses

8y^2-2y^2-5y-7y-11+7=0

We add all the numbers together, and all the variables

6y^2-12y-4=0

a = 6; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·6·(-4)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*6}=\frac{12-4\sqrt{15}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*6}=\frac{12+4\sqrt{15}}{12}
$