2x^2+40x+5000=14600

Solution for 2x^2+40x+5000=14600 equation:

2x^2+40x+5000=14600

We move all terms to the left:

2x^2+40x+5000-(14600)=0

We add all the numbers together, and all the variables

2x^2+40x-9600=0

a = 2; b = 40; c = -9600;
Δ = b2-4ac
Δ = 402-4·2·(-9600)
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-280}{2*2}=\frac{-320}{4}
=-80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+280}{2*2}=\frac{240}{4}
=60
$