5x^2+487=-100x-3

Solution for 5x^2+487=-100x-3 equation:

5x^2+487=-100x-3

We move all terms to the left:

5x^2+487-(-100x-3)=0

We get rid of parentheses

5x^2+100x+3+487=0

We add all the numbers together, and all the variables

5x^2+100x+490=0

a = 5; b = 100; c = +490;
Δ = b2-4ac
Δ = 1002-4·5·490
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{2}}{2*5}=\frac{-100-10\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{2}}{2*5}=\frac{-100+10\sqrt{2}}{10}
$