420=15x+x^2

Solution for 420=15x+x^2 equation:

420=15x+x^2

We move all terms to the left:

420-(15x+x^2)=0

We get rid of parentheses

-x^2-15x+420=0

We add all the numbers together, and all the variables

-1x^2-15x+420=0

a = -1; b = -15; c = +420;
Δ = b2-4ac
Δ = -152-4·(-1)·420
Δ = 1905
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{1905}}{2*-1}=\frac{15-\sqrt{1905}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1905}}{2*-1}=\frac{15+\sqrt{1905}}{-2}
$