x2+29x+120=0

Solution for x2+29x+120=0 equation:

x2+29x+120=0

We add all the numbers together, and all the variables

x^2+29x+120=0

a = 1; b = 29; c = +120;
Δ = b2-4ac
Δ = 292-4·1·120
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-19}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+19}{2*1}=\frac{-10}{2}
=-5
$