x2+16x=420

Solution for x2+16x=420 equation:

x2+16x=420

We move all terms to the left:

x2+16x-(420)=0

We add all the numbers together, and all the variables

x^2+16x-420=0

a = 1; b = 16; c = -420;
Δ = b2-4ac
Δ = 162-4·1·(-420)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-44}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+44}{2*1}=\frac{28}{2}
=14
$