(y+4)(y+6)=120

Solution for (y+4)(y+6)=120 equation:

(y+4)(y+6)=120

We move all terms to the left:

(y+4)(y+6)-(120)=0

We multiply parentheses ..

(+y^2+6y+4y+24)-120=0

We get rid of parentheses

y^2+6y+4y+24-120=0

We add all the numbers together, and all the variables

y^2+10y-96=0

a = 1; b = 10; c = -96;
Δ = b2-4ac
Δ = 102-4·1·(-96)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-22}{2*1}=\frac{-32}{2}
=-16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+22}{2*1}=\frac{12}{2}
=6
$