4a(a+7)=120

Solution for 4a(a+7)=120 equation:

4a(a+7)=120

We move all terms to the left:

4a(a+7)-(120)=0

We multiply parentheses

4a^2+28a-120=0

a = 4; b = 28; c = -120;
Δ = b2-4ac
Δ = 282-4·4·(-120)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-52}{2*4}=\frac{-80}{8}
=-10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+52}{2*4}=\frac{24}{8}
=3
$