5x^2+470=-100x

Solution for 5x^2+470=-100x equation:

5x^2+470=-100x

We move all terms to the left:

5x^2+470-(-100x)=0

We get rid of parentheses

5x^2+100x+470=0

a = 5; b = 100; c = +470;
Δ = b2-4ac
Δ = 1002-4·5·470
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{6}}{2*5}=\frac{-100-10\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{6}}{2*5}=\frac{-100+10\sqrt{6}}{10}
$