y^2+7y+2=80

Solution for y^2+7y+2=80 equation:

y^2+7y+2=80

We move all terms to the left:

y^2+7y+2-(80)=0

We add all the numbers together, and all the variables

y^2+7y-78=0

a = 1; b = 7; c = -78;
Δ = b2-4ac
Δ = 72-4·1·(-78)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*1}=\frac{-26}{2}
=-13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*1}=\frac{12}{2}
=6
$