5y^2+3(y+2)=54

Solution for 5y^2+3(y+2)=54 equation:

5y^2+3(y+2)=54

We move all terms to the left:

5y^2+3(y+2)-(54)=0

We multiply parentheses

5y^2+3y+6-54=0

We add all the numbers together, and all the variables

5y^2+3y-48=0

a = 5; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·5·(-48)
Δ = 969
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{-(3)-\sqrt{969}}{2*5}=\frac{-3-\sqrt{969}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{969}}{2*5}=\frac{-3+\sqrt{969}}{10}
$