5(y^2+y+8)=6y^2+6y+13

Solution for 5(y^2+y+8)=6y^2+6y+13 equation:

5(y^2+y+8)=6y^2+6y+13

We move all terms to the left:

5(y^2+y+8)-(6y^2+6y+13)=0

We multiply parentheses

5y^2+5y-(6y^2+6y+13)+40=0

We get rid of parentheses

5y^2-6y^2+5y-6y-13+40=0

We add all the numbers together, and all the variables

-1y^2-1y+27=0

a = -1; b = -1; c = +27;
Δ = b2-4ac
Δ = -12-4·(-1)·27
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{109}}{2*-1}=\frac{1-\sqrt{109}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{109}}{2*-1}=\frac{1+\sqrt{109}}{-2}
$