x*x+3x-40=420

Solution for x*x+3x-40=420 equation:

x*x+3x-40=420

We move all terms to the left:

x*x+3x-40-(420)=0

We add all the numbers together, and all the variables

3x+x*x-460=0

Wy multiply elements

x^2+3x-460=0

a = 1; b = 3; c = -460;
Δ = b2-4ac
Δ = 32-4·1·(-460)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-43}{2*1}=\frac{-46}{2}
=-23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+43}{2*1}=\frac{40}{2}
=20
$